[{"date_updated":"2026-03-03T08:49:33Z","author":[{"last_name":"Jalowy","orcid":"0000-0001-9624-2685","full_name":"Jalowy, Jonas","id":"113768","first_name":"Jonas"},{"last_name":"Lammers","full_name":"Lammers, Isabel","first_name":"Isabel"},{"last_name":"Löwe","full_name":"Löwe, Matthias","first_name":"Matthias"}],"date_created":"2026-03-03T08:49:16Z","title":"The infinite block spin Ising model","year":"2026","citation":{"ama":"Jalowy J, Lammers I, Löwe M. The infinite block spin Ising model. <i>arXiv:260301994</i>. Published online 2026.","chicago":"Jalowy, Jonas, Isabel Lammers, and Matthias Löwe. “The Infinite Block Spin Ising Model.” <i>ArXiv:2603.01994</i>, 2026.","ieee":"J. Jalowy, I. Lammers, and M. Löwe, “The infinite block spin Ising model,” <i>arXiv:2603.01994</i>. 2026.","bibtex":"@article{Jalowy_Lammers_Löwe_2026, title={The infinite block spin Ising model}, journal={arXiv:2603.01994}, author={Jalowy, Jonas and Lammers, Isabel and Löwe, Matthias}, year={2026} }","short":"J. Jalowy, I. Lammers, M. Löwe, ArXiv:2603.01994 (2026).","mla":"Jalowy, Jonas, et al. “The Infinite Block Spin Ising Model.” <i>ArXiv:2603.01994</i>, 2026.","apa":"Jalowy, J., Lammers, I., &#38; Löwe, M. (2026). The infinite block spin Ising model. In <i>arXiv:2603.01994</i>."},"_id":"64816","external_id":{"arxiv":["2603.01994"]},"user_id":"113768","department":[{"_id":"94"}],"language":[{"iso":"eng"}],"type":"preprint","publication":"arXiv:2603.01994","abstract":[{"text":"We study a block mean-field Ising model with $N$ spins split into $s_N$ blocks, with Curie-Weiss interaction within blocks and nearest-neighbor coupling between blocks. While previous models deal with the block magnetization for a fixed number of blocks, we study the the simultaneous limit $N\\to\\infty$ and $s_N\\to\\infty$. The model interpolates between Curie-Weiss model for $s_N=1$, multi-species mean field for fixed $s_N=s$, and the 1D Ising model for each spin in its own block at $s_N=N$.\r\n  Under mild growth conditions on $s_N$, we prove a law of large numbers and a multivariate CLT with covariance given by the lattice Green's function. For instance, the high temperature CLT essentially covers the optimal range up to $s_N=o(N/(\\log N)^c)$ and the low temperature regime is new even for fixed number of blocks $s > 2$. In addition to the standard competition between entropy and energy, a new obstacle in the proofs is a curse of dimensionality as $s_N \\to \\infty$.","lang":"eng"}],"status":"public"},{"language":[{"iso":"eng"}],"_id":"59664","external_id":{"arxiv":["2504.11593"]},"user_id":"113768","department":[{"_id":"94"}],"abstract":[{"text":"Given a sequence of polynomials $(P_n)_{n \\in \\mathbb{N}}$ with only\r\nnonpositive zeros, the aim of this article is to present a user-friendly\r\napproach for determining the limiting zero distribution of $P_n$ as\r\n$\\mathrm{deg}\\, P_n \\to \\infty$. The method is based on establishing an\r\nequivalence between the existence of a limiting empirical zero distribution\r\n$\\mu$ and the existence of an exponential profile $g$ associated with the\r\ncoefficients of the polynomials $(P_n)_{n \\in \\mathbb{N}}$. The exponential\r\nprofile $g$, which can be roughly described by $[z^k]P_n(z) \\approx \\exp(n\r\ng(k/n))$, offers a direct route to computing the Cauchy transform $G$ of $\\mu$:\r\nthe functions $t \\mapsto tG(t)$ and $\\alpha \\mapsto \\exp(-g'(\\alpha))$ are\r\nmutual inverses. This relationship, in various forms, has previously appeared\r\nin the literature, most notably in the paper [Van Assche, Fano and Ortolani,\r\nSIAM J. Math. Anal., 1987].\r\n  As a first contribution, we present a self-contained probabilistic proof of\r\nthis equivalence by representing the polynomials as generating functions of\r\nsums of independent Bernoulli random variables. This probabilistic framework\r\nnaturally lends itself to tools from large deviation theory, such as the\r\nexponential change of measure. The resulting theorems generalize and unify a\r\nrange of previously known results, which were traditionally established through\r\nanalytic or combinatorial methods.\r\n  Secondly, using the profile-based approach, we investigate how the\r\nexponential profile and the limiting zero distribution behave under certain\r\noperations on polynomials, including finite free convolutions, Hadamard\r\nproducts, and repeated differentiation. In particular, our approach yields new\r\nproofs of the convergence results `$\\boxplus_n \\to \\boxplus$' and `$\\boxtimes_n\r\n\\to \\boxtimes$', extending them to cases where the distributions are not\r\nnecessarily compactly supported.","lang":"eng"}],"status":"public","type":"preprint","publication":"arXiv:2504.11593","title":"Zeros and exponential profiles of polynomials I: Limit distributions,  finite free convolutions and repeated differentiation","date_updated":"2025-04-23T14:38:04Z","author":[{"orcid":"0000-0001-9624-2685","last_name":"Jalowy","id":"113768","full_name":"Jalowy, Jonas","first_name":"Jonas"},{"first_name":"Zakhar","last_name":"Kabluchko","full_name":"Kabluchko, Zakhar"},{"last_name":"Marynych","full_name":"Marynych, Alexander","first_name":"Alexander"}],"date_created":"2025-04-23T14:37:41Z","year":"2025","citation":{"apa":"Jalowy, J., Kabluchko, Z., &#38; Marynych, A. (2025). Zeros and exponential profiles of polynomials I: Limit distributions,  finite free convolutions and repeated differentiation. In <i>arXiv:2504.11593</i>.","mla":"Jalowy, Jonas, et al. “Zeros and Exponential Profiles of Polynomials I: Limit Distributions,  Finite Free Convolutions and Repeated Differentiation.” <i>ArXiv:2504.11593</i>, 2025.","bibtex":"@article{Jalowy_Kabluchko_Marynych_2025, title={Zeros and exponential profiles of polynomials I: Limit distributions,  finite free convolutions and repeated differentiation}, journal={arXiv:2504.11593}, author={Jalowy, Jonas and Kabluchko, Zakhar and Marynych, Alexander}, year={2025} }","short":"J. Jalowy, Z. Kabluchko, A. Marynych, ArXiv:2504.11593 (2025).","chicago":"Jalowy, Jonas, Zakhar Kabluchko, and Alexander Marynych. “Zeros and Exponential Profiles of Polynomials I: Limit Distributions,  Finite Free Convolutions and Repeated Differentiation.” <i>ArXiv:2504.11593</i>, 2025.","ieee":"J. Jalowy, Z. Kabluchko, and A. Marynych, “Zeros and exponential profiles of polynomials I: Limit distributions,  finite free convolutions and repeated differentiation,” <i>arXiv:2504.11593</i>. 2025.","ama":"Jalowy J, Kabluchko Z, Marynych A. Zeros and exponential profiles of polynomials I: Limit distributions,  finite free convolutions and repeated differentiation. <i>arXiv:250411593</i>. Published online 2025."}},{"status":"public","type":"journal_article","publication":"Journal of Functional Analysis","language":[{"iso":"eng"}],"article_number":"110974","user_id":"113768","department":[{"_id":"94"}],"_id":"59665","citation":{"apa":"Erbar, M., Huesmann, M., Jalowy, J., &#38; Müller, B. (2025). Optimal transport of stationary point processes: Metric structure, gradient flow and convexity of the specific entropy. <i>Journal of Functional Analysis</i>, <i>289</i>(4), Article 110974. <a href=\"https://doi.org/10.1016/j.jfa.2025.110974\">https://doi.org/10.1016/j.jfa.2025.110974</a>","mla":"Erbar, Matthias, et al. “Optimal Transport of Stationary Point Processes: Metric Structure, Gradient Flow and Convexity of the Specific Entropy.” <i>Journal of Functional Analysis</i>, vol. 289, no. 4, 110974, Elsevier BV, 2025, doi:<a href=\"https://doi.org/10.1016/j.jfa.2025.110974\">10.1016/j.jfa.2025.110974</a>.","bibtex":"@article{Erbar_Huesmann_Jalowy_Müller_2025, title={Optimal transport of stationary point processes: Metric structure, gradient flow and convexity of the specific entropy}, volume={289}, DOI={<a href=\"https://doi.org/10.1016/j.jfa.2025.110974\">10.1016/j.jfa.2025.110974</a>}, number={4110974}, journal={Journal of Functional Analysis}, publisher={Elsevier BV}, author={Erbar, Matthias and Huesmann, Martin and Jalowy, Jonas and Müller, Bastian}, year={2025} }","short":"M. Erbar, M. Huesmann, J. Jalowy, B. Müller, Journal of Functional Analysis 289 (2025).","ama":"Erbar M, Huesmann M, Jalowy J, Müller B. Optimal transport of stationary point processes: Metric structure, gradient flow and convexity of the specific entropy. <i>Journal of Functional Analysis</i>. 2025;289(4). doi:<a href=\"https://doi.org/10.1016/j.jfa.2025.110974\">10.1016/j.jfa.2025.110974</a>","ieee":"M. Erbar, M. Huesmann, J. Jalowy, and B. Müller, “Optimal transport of stationary point processes: Metric structure, gradient flow and convexity of the specific entropy,” <i>Journal of Functional Analysis</i>, vol. 289, no. 4, Art. no. 110974, 2025, doi: <a href=\"https://doi.org/10.1016/j.jfa.2025.110974\">10.1016/j.jfa.2025.110974</a>.","chicago":"Erbar, Matthias, Martin Huesmann, Jonas Jalowy, and Bastian Müller. “Optimal Transport of Stationary Point Processes: Metric Structure, Gradient Flow and Convexity of the Specific Entropy.” <i>Journal of Functional Analysis</i> 289, no. 4 (2025). <a href=\"https://doi.org/10.1016/j.jfa.2025.110974\">https://doi.org/10.1016/j.jfa.2025.110974</a>."},"intvolume":"       289","year":"2025","issue":"4","publication_status":"published","publication_identifier":{"issn":["0022-1236"]},"doi":"10.1016/j.jfa.2025.110974","title":"Optimal transport of stationary point processes: Metric structure, gradient flow and convexity of the specific entropy","author":[{"first_name":"Matthias","full_name":"Erbar, Matthias","last_name":"Erbar"},{"full_name":"Huesmann, Martin","last_name":"Huesmann","first_name":"Martin"},{"first_name":"Jonas","id":"113768","full_name":"Jalowy, Jonas","orcid":"0000-0001-9624-2685","last_name":"Jalowy"},{"first_name":"Bastian","last_name":"Müller","full_name":"Müller, Bastian"}],"date_created":"2025-04-23T14:39:50Z","volume":289,"publisher":"Elsevier BV","date_updated":"2025-04-23T14:41:19Z"},{"publication":"arXiv:2506.13661","type":"preprint","abstract":[{"lang":"eng","text":"In this work, we present a complete characterization of the covariance\r\nstructure of number statistics in boxes for hyperuniform point processes. Under\r\na standard integrability assumption, the covariance depends solely on the\r\noverlap of the faces of the box. Beyond this assumption, a novel interpolating\r\ncovariance structure emerges. This enables us to identify a limiting Gaussian\r\n'coarse-grained' process, counting the number of points in large boxes as a\r\nfunction of the box position. Depending on the integrability assumption, this\r\nprocess may be continuous or discontinuous, e.g. in d=1 it is given by an\r\nincrement process of a fractional Brownian motion."}],"status":"public","external_id":{"arxiv":["2506.13661"]},"_id":"60293","department":[{"_id":"94"}],"user_id":"113768","language":[{"iso":"eng"}],"year":"2025","citation":{"apa":"Jalowy, J., &#38; Stange, H. (2025). Box-Covariances of Hyperuniform Point Processes. In <i>arXiv:2506.13661</i>.","bibtex":"@article{Jalowy_Stange_2025, title={Box-Covariances of Hyperuniform Point Processes}, journal={arXiv:2506.13661}, author={Jalowy, Jonas and Stange, Hanna}, year={2025} }","mla":"Jalowy, Jonas, and Hanna Stange. “Box-Covariances of Hyperuniform Point Processes.” <i>ArXiv:2506.13661</i>, 2025.","short":"J. Jalowy, H. Stange, ArXiv:2506.13661 (2025).","ama":"Jalowy J, Stange H. Box-Covariances of Hyperuniform Point Processes. <i>arXiv:250613661</i>. Published online 2025.","ieee":"J. Jalowy and H. Stange, “Box-Covariances of Hyperuniform Point Processes,” <i>arXiv:2506.13661</i>. 2025.","chicago":"Jalowy, Jonas, and Hanna Stange. “Box-Covariances of Hyperuniform Point Processes.” <i>ArXiv:2506.13661</i>, 2025."},"date_updated":"2025-06-22T08:03:20Z","author":[{"full_name":"Jalowy, Jonas","id":"113768","orcid":"0000-0001-9624-2685","last_name":"Jalowy","first_name":"Jonas"},{"first_name":"Hanna","full_name":"Stange, Hanna","last_name":"Stange"}],"date_created":"2025-06-22T08:02:28Z","title":"Box-Covariances of Hyperuniform Point Processes"},{"abstract":[{"text":"Differential equations posed on quadratic matrix Lie groups arise in the context of classical mechanics and quantum dynamical systems. Lie group numerical integrators preserve the constants of motions defining the Lie group. Thus, they respect important physical laws of the dynamical system, such as unitarity and energy conservation in the context of quantum dynamical systems, for instance. In this article we develop a high-order commutator free Lie group integrator for non-autonomous differential equations evolving on quadratic Lie groups. Instead of matrix exponentials, which are expensive to evaluate and need to be approximated by appropriate rational functions in order to preserve the Lie group structure, the proposed method is obtained as a composition of Cayley transforms which naturally respect the structure of quadratic Lie groups while being computationally efficient to evaluate. Unlike Cayley-Magnus methods the method is also free from nested matrix commutators.","lang":"eng"}],"status":"public","publication":"J. Comput. Appl. Math","type":"journal_article","language":[{"iso":"eng"}],"_id":"59507","department":[{"_id":"94"}],"user_id":"95394","year":"2025","intvolume":"       477","citation":{"mla":"Wembe Moafo, Boris Edgar, et al. “Commutator-Free Cayley Methods.” <i>J. Comput. Appl. Math</i>, vol. 477, no. 15, doi:<a href=\"https://doi.org/10.1016/j.cam.2025.117184\">10.1016/j.cam.2025.117184</a>.","short":"B.E. Wembe Moafo, C. Offen, S. Maslovskaya, S. Ober-Blöbaum, P. Singh, J. Comput. Appl. Math 477 (n.d.).","bibtex":"@article{Wembe Moafo_Offen_Maslovskaya_Ober-Blöbaum_Singh, title={Commutator-free Cayley methods}, volume={477}, DOI={<a href=\"https://doi.org/10.1016/j.cam.2025.117184\">10.1016/j.cam.2025.117184</a>}, number={15}, journal={J. Comput. Appl. Math}, author={Wembe Moafo, Boris Edgar and Offen, Cristian  and Maslovskaya, Sofya and Ober-Blöbaum, Sina and Singh, Pranav} }","apa":"Wembe Moafo, B. E., Offen, C., Maslovskaya, S., Ober-Blöbaum, S., &#38; Singh, P. (n.d.). Commutator-free Cayley methods. <i>J. Comput. Appl. Math</i>, <i>477</i>(15). <a href=\"https://doi.org/10.1016/j.cam.2025.117184\">https://doi.org/10.1016/j.cam.2025.117184</a>","ieee":"B. E. Wembe Moafo, C. Offen, S. Maslovskaya, S. Ober-Blöbaum, and P. Singh, “Commutator-free Cayley methods,” <i>J. Comput. Appl. Math</i>, vol. 477, no. 15, doi: <a href=\"https://doi.org/10.1016/j.cam.2025.117184\">10.1016/j.cam.2025.117184</a>.","chicago":"Wembe Moafo, Boris Edgar, Cristian  Offen, Sofya Maslovskaya, Sina Ober-Blöbaum, and Pranav Singh. “Commutator-Free Cayley Methods.” <i>J. Comput. Appl. Math</i> 477, no. 15 (n.d.). <a href=\"https://doi.org/10.1016/j.cam.2025.117184\">https://doi.org/10.1016/j.cam.2025.117184</a>.","ama":"Wembe Moafo BE, Offen C, Maslovskaya S, Ober-Blöbaum S, Singh P. Commutator-free Cayley methods. <i>J Comput Appl Math</i>. 477(15). doi:<a href=\"https://doi.org/10.1016/j.cam.2025.117184\">10.1016/j.cam.2025.117184</a>"},"publication_status":"submitted","issue":"15","title":"Commutator-free Cayley methods","doi":"10.1016/j.cam.2025.117184","date_updated":"2025-12-16T15:17:27Z","volume":477,"author":[{"first_name":"Boris Edgar","last_name":"Wembe Moafo","id":"95394","full_name":"Wembe Moafo, Boris Edgar"},{"first_name":"Cristian ","last_name":"Offen","full_name":"Offen, Cristian "},{"first_name":"Sofya","id":"87909","full_name":"Maslovskaya, Sofya","last_name":"Maslovskaya"},{"first_name":"Sina","id":"16494","full_name":"Ober-Blöbaum, Sina","last_name":"Ober-Blöbaum"},{"first_name":"Pranav","last_name":"Singh","full_name":"Singh, Pranav"}],"date_created":"2025-04-10T14:42:52Z"},{"citation":{"chicago":"Byun, Sung-Soo, Jonas Jalowy, Yong-Woo Lee, and Grégory Schehr. “Moderate-to-Large Deviation Asymptotics for Real Eigenvalues of the Elliptic Ginibre Matrices.” <i>ArXiv:2511.09191</i>, 2025.","ieee":"S.-S. Byun, J. Jalowy, Y.-W. Lee, and G. Schehr, “Moderate-to-large deviation asymptotics for real eigenvalues of the elliptic Ginibre matrices,” <i>arXiv:2511.09191</i>. 2025.","ama":"Byun S-S, Jalowy J, Lee Y-W, Schehr G. Moderate-to-large deviation asymptotics for real eigenvalues of the elliptic Ginibre matrices. <i>arXiv:251109191</i>. Published online 2025.","apa":"Byun, S.-S., Jalowy, J., Lee, Y.-W., &#38; Schehr, G. (2025). Moderate-to-large deviation asymptotics for real eigenvalues of the elliptic Ginibre matrices. In <i>arXiv:2511.09191</i>.","bibtex":"@article{Byun_Jalowy_Lee_Schehr_2025, title={Moderate-to-large deviation asymptotics for real eigenvalues of the elliptic Ginibre matrices}, journal={arXiv:2511.09191}, author={Byun, Sung-Soo and Jalowy, Jonas and Lee, Yong-Woo and Schehr, Grégory}, year={2025} }","short":"S.-S. Byun, J. Jalowy, Y.-W. Lee, G. Schehr, ArXiv:2511.09191 (2025).","mla":"Byun, Sung-Soo, et al. “Moderate-to-Large Deviation Asymptotics for Real Eigenvalues of the Elliptic Ginibre Matrices.” <i>ArXiv:2511.09191</i>, 2025."},"year":"2025","date_created":"2025-12-22T08:37:02Z","author":[{"first_name":"Sung-Soo","last_name":"Byun","full_name":"Byun, Sung-Soo"},{"first_name":"Jonas","last_name":"Jalowy","orcid":"0000-0001-9624-2685","id":"113768","full_name":"Jalowy, Jonas"},{"first_name":"Yong-Woo","full_name":"Lee, Yong-Woo","last_name":"Lee"},{"full_name":"Schehr, Grégory","last_name":"Schehr","first_name":"Grégory"}],"date_updated":"2025-12-22T08:37:35Z","title":"Moderate-to-large deviation asymptotics for real eigenvalues of the elliptic Ginibre matrices","publication":"arXiv:2511.09191","type":"preprint","status":"public","abstract":[{"text":"We study the statistics of the number of real eigenvalues in the elliptic deformation of the real Ginibre ensemble. As the matrix dimension grows, the law of large numbers and the central limit theorem for the number of real eigenvalues are well understood, but the probabilities of rare events remain largely unexplored. Large deviation type results have been obtained only in extreme cases, when either a vanishingly small proportion of eigenvalues are real or almost all eigenvalues are real. Here, in both the strong and weak asymmetry regimes, we derive the probabilities of rare events in the moderate-to-large deviation regime, thereby providing a natural connection between the previously known regime of Gaussian fluctuations and the large deviation regime. Our results are new even for the classical real Ginibre ensemble.","lang":"eng"}],"department":[{"_id":"94"}],"user_id":"113768","_id":"63394","external_id":{"arxiv":["2511.09191"]},"language":[{"iso":"eng"}]},{"title":"Zeros of polynomial powers under the heat flow","author":[{"full_name":"Höfert, Antonia","last_name":"Höfert","first_name":"Antonia"},{"first_name":"Jonas","full_name":"Jalowy, Jonas","id":"113768","last_name":"Jalowy","orcid":"0000-0001-9624-2685"},{"full_name":"Kabluchko, Zakhar","last_name":"Kabluchko","first_name":"Zakhar"}],"date_created":"2025-12-22T08:36:24Z","date_updated":"2025-12-22T08:36:46Z","citation":{"short":"A. Höfert, J. Jalowy, Z. Kabluchko, ArXiv:2512.17808 (2025).","mla":"Höfert, Antonia, et al. “Zeros of Polynomial Powers under the Heat Flow.” <i>ArXiv:2512.17808</i>, 2025.","bibtex":"@article{Höfert_Jalowy_Kabluchko_2025, title={Zeros of polynomial powers under the heat flow}, journal={arXiv:2512.17808}, author={Höfert, Antonia and Jalowy, Jonas and Kabluchko, Zakhar}, year={2025} }","apa":"Höfert, A., Jalowy, J., &#38; Kabluchko, Z. (2025). Zeros of polynomial powers under the heat flow. In <i>arXiv:2512.17808</i>.","ama":"Höfert A, Jalowy J, Kabluchko Z. Zeros of polynomial powers under the heat flow. <i>arXiv:251217808</i>. Published online 2025.","ieee":"A. Höfert, J. Jalowy, and Z. Kabluchko, “Zeros of polynomial powers under the heat flow,” <i>arXiv:2512.17808</i>. 2025.","chicago":"Höfert, Antonia, Jonas Jalowy, and Zakhar Kabluchko. “Zeros of Polynomial Powers under the Heat Flow.” <i>ArXiv:2512.17808</i>, 2025."},"year":"2025","language":[{"iso":"eng"}],"department":[{"_id":"94"}],"user_id":"113768","_id":"63393","external_id":{"arxiv":["2512.17808"]},"status":"public","abstract":[{"lang":"eng","text":"We study the evolution of zeros of high polynomial powers under the heat flow. For any fixed polynomial $P(z)$, we prove that the empirical zero distribution of its heat-evolved $n$-th power converges to a distribution on the complex plane as $n$ tends to infinity. We describe this limit distribution $μ_t$ as a function of the time parameter $t$ of the heat evolution: For small time, zeros start to spread out in approximately semicircular distributions, then intricate curves start to form and merge, until for large time, the zero distribution approaches a widespread semicircle law through the initial center of mass. The Stieltjes transform of the limit distribution $μ_t$ satisfies a self-consistent equation and a Burgers' equation. The present paper deals with general complex-rooted polynomials for which, in contrast to the real-rooted case, no free-probabilistic representation for $μ_t$ is available."}],"publication":"arXiv:2512.17808","type":"preprint"},{"citation":{"bibtex":"@article{Zeros and exponential profiles of polynomials II: Examples_2025, DOI={<a href=\"https://doi.org/10.48550/ARXIV.2509.11248\">10.48550/ARXIV.2509.11248</a>}, year={2025} }","mla":"<i>Zeros and Exponential Profiles of Polynomials II: Examples</i>. 2025, doi:<a href=\"https://doi.org/10.48550/ARXIV.2509.11248\">10.48550/ARXIV.2509.11248</a>.","short":"(2025).","apa":"<i>Zeros and exponential profiles of polynomials II: Examples</i>. (2025). <a href=\"https://doi.org/10.48550/ARXIV.2509.11248\">https://doi.org/10.48550/ARXIV.2509.11248</a>","ama":"Zeros and exponential profiles of polynomials II: Examples. Published online 2025. doi:<a href=\"https://doi.org/10.48550/ARXIV.2509.11248\">10.48550/ARXIV.2509.11248</a>","ieee":"“Zeros and exponential profiles of polynomials II: Examples,” 2025, doi: <a href=\"https://doi.org/10.48550/ARXIV.2509.11248\">10.48550/ARXIV.2509.11248</a>.","chicago":"“Zeros and Exponential Profiles of Polynomials II: Examples,” 2025. <a href=\"https://doi.org/10.48550/ARXIV.2509.11248\">https://doi.org/10.48550/ARXIV.2509.11248</a>."},"year":"2025","doi":"10.48550/ARXIV.2509.11248","title":"Zeros and exponential profiles of polynomials II: Examples","date_created":"2025-11-24T13:55:55Z","date_updated":"2026-03-19T14:45:35Z","status":"public","abstract":[{"text":"In [Jalowy, Kabluchko, Marynych, arXiv:2504.11593v1, 2025], the authors discuss a user-friendly approach to determine the limiting empirical zero distribution of a sequence of real-rooted polynomials, as the degree goes to $\\infty$. In this note, we aim to apply it to a vast range of examples of polynomials providing a unifying source for limiting empirical zero distributions.\n We cover Touchard, Fubini, Eulerian, Narayana and little $q$-Laguerre polynomials as well as hypergeometric polynomials including the classical Hermite, Laguerre and Jacobi polynomials. We construct polynomials whose empirical zero distributions converge to the free multiplicative normal and Poisson distributions. Furthermore, we study polynomials generated by some differential operators. As one inverse result, we derive coefficient asymptotics of the characteristic polynomial of random covariance matrices.","lang":"eng"}],"type":"journal_article","department":[{"_id":"94"}],"user_id":"113768","_id":"62291"},{"citation":{"apa":"Berger, T., Dennstädt, D., Lanza, L., &#38; Worthmann, K. (2024). Robust Funnel Model Predictive Control for Output Tracking with Prescribed Performance. <i>SIAM Journal on Control and Optimization</i>.","short":"T. Berger, D. Dennstädt, L. Lanza, K. Worthmann, SIAM Journal on Control and Optimization (2024).","mla":"Berger, Thomas, et al. “Robust Funnel Model Predictive Control for Output Tracking with Prescribed Performance.” <i>SIAM Journal on Control and Optimization</i>, 2024.","bibtex":"@article{Berger_Dennstädt_Lanza_Worthmann_2024, title={Robust Funnel Model Predictive Control for Output Tracking with Prescribed Performance}, journal={SIAM Journal on Control and Optimization}, author={Berger, Thomas and Dennstädt, Dario and Lanza, L.  and Worthmann, K. }, year={2024} }","chicago":"Berger, Thomas, Dario Dennstädt, L.  Lanza, and K.  Worthmann. “Robust Funnel Model Predictive Control for Output Tracking with Prescribed Performance.” <i>SIAM Journal on Control and Optimization</i>, 2024.","ieee":"T. Berger, D. Dennstädt, L. Lanza, and K. Worthmann, “Robust Funnel Model Predictive Control for Output Tracking with Prescribed Performance,” <i>SIAM Journal on Control and Optimization</i>, 2024.","ama":"Berger T, Dennstädt D, Lanza L, Worthmann K. Robust Funnel Model Predictive Control for Output Tracking with Prescribed Performance. <i>SIAM Journal on Control and Optimization</i>. Published online 2024."},"status":"public","year":"2024","type":"journal_article","publication":"SIAM Journal on Control and Optimization","language":[{"iso":"eng"}],"title":"Robust Funnel Model Predictive Control for Output Tracking with Prescribed Performance","date_created":"2024-04-03T10:08:01Z","user_id":"77457","author":[{"last_name":"Berger","id":"77457","full_name":"Berger, Thomas","first_name":"Thomas"},{"first_name":"Dario","last_name":"Dennstädt","full_name":"Dennstädt, Dario","id":"98033"},{"first_name":"L. ","last_name":"Lanza","full_name":"Lanza, L. "},{"first_name":"K. ","last_name":"Worthmann","full_name":"Worthmann, K. "}],"department":[{"_id":"618"}],"date_updated":"2026-01-05T20:52:17Z","_id":"53146"},{"_id":"53142","department":[{"_id":"618"}],"user_id":"77457","language":[{"iso":"eng"}],"publication":"IMA Journal of Mathematical Control and Information,","type":"journal_article","status":"public","date_updated":"2024-04-05T05:50:29Z","volume":40,"author":[{"first_name":"Thomas","full_name":"Berger, Thomas","id":"77457","last_name":"Berger"},{"first_name":"Lukas","last_name":"Lanza","full_name":"Lanza, Lukas"}],"date_created":"2024-04-03T09:37:59Z","title":"Funnel control of linear systems with arbitrary relative degree under output measurement losses","doi":"doi: 10.1093/imamci/dnad029","issue":"4","year":"2023","page":"691-713","intvolume":"        40","citation":{"chicago":"Berger, Thomas, and Lukas Lanza. “Funnel Control of Linear Systems with Arbitrary Relative Degree under Output Measurement Losses.” <i>IMA Journal of Mathematical Control and Information,</i> 40, no. 4 (2023): 691–713. <a href=\"https://doi.org/doi: 10.1093/imamci/dnad029\">https://doi.org/doi: 10.1093/imamci/dnad029</a>.","ieee":"T. Berger and L. Lanza, “Funnel control of linear systems with arbitrary relative degree under output measurement losses,” <i>IMA Journal of Mathematical Control and Information,</i> vol. 40, no. 4, pp. 691–713, 2023, doi: <a href=\"https://doi.org/doi: 10.1093/imamci/dnad029\">doi: 10.1093/imamci/dnad029</a>.","ama":"Berger T, Lanza L. Funnel control of linear systems with arbitrary relative degree under output measurement losses. <i>IMA Journal of Mathematical Control and Information,</i>. 2023;40(4):691-713. doi:<a href=\"https://doi.org/doi: 10.1093/imamci/dnad029\">doi: 10.1093/imamci/dnad029</a>","apa":"Berger, T., &#38; Lanza, L. (2023). Funnel control of linear systems with arbitrary relative degree under output measurement losses. <i>IMA Journal of Mathematical Control and Information,</i> <i>40</i>(4), 691–713. <a href=\"https://doi.org/doi: 10.1093/imamci/dnad029\">https://doi.org/doi: 10.1093/imamci/dnad029</a>","bibtex":"@article{Berger_Lanza_2023, title={Funnel control of linear systems with arbitrary relative degree under output measurement losses}, volume={40}, DOI={<a href=\"https://doi.org/doi: 10.1093/imamci/dnad029\">doi: 10.1093/imamci/dnad029</a>}, number={4}, journal={IMA Journal of Mathematical Control and Information,}, author={Berger, Thomas and Lanza, Lukas}, year={2023}, pages={691–713} }","short":"T. Berger, L. Lanza, IMA Journal of Mathematical Control and Information, 40 (2023) 691–713.","mla":"Berger, Thomas, and Lukas Lanza. “Funnel Control of Linear Systems with Arbitrary Relative Degree under Output Measurement Losses.” <i>IMA Journal of Mathematical Control and Information,</i> vol. 40, no. 4, 2023, pp. 691–713, doi:<a href=\"https://doi.org/doi: 10.1093/imamci/dnad029\">doi: 10.1093/imamci/dnad029</a>."}},{"doi":"doi: 10.1016/j.automatica.2023.111204 (open access)","title":"Edge-wise funnel output synchronization of heterogeneous agents with relative degree one","volume":156,"author":[{"last_name":"Lee","full_name":"Lee, J. G.","first_name":"J. G."},{"first_name":"Thomas","last_name":"Berger","full_name":"Berger, Thomas","id":"77457"},{"first_name":"S.","full_name":"Trenn, S.","last_name":"Trenn"},{"first_name":"H.","full_name":"Shim, H.","last_name":"Shim"}],"date_created":"2024-04-03T09:56:35Z","date_updated":"2024-04-05T05:52:28Z","page":"Article 111204","intvolume":"       156","citation":{"ama":"Lee JG, Berger T, Trenn S, Shim H. Edge-wise funnel output synchronization of heterogeneous agents with relative degree one. <i>Automatica</i>. 2023;156:Article 111204. doi:<a href=\"https://doi.org/doi: 10.1016/j.automatica.2023.111204 (open access)\">doi: 10.1016/j.automatica.2023.111204 (open access)</a>","chicago":"Lee, J. G., Thomas Berger, S. Trenn, and H. Shim. “Edge-Wise Funnel Output Synchronization of Heterogeneous Agents with Relative Degree One.” <i>Automatica</i> 156 (2023): Article 111204. <a href=\"https://doi.org/doi: 10.1016/j.automatica.2023.111204 (open access)\">https://doi.org/doi: 10.1016/j.automatica.2023.111204 (open access)</a>.","ieee":"J. G. Lee, T. Berger, S. Trenn, and H. Shim, “Edge-wise funnel output synchronization of heterogeneous agents with relative degree one,” <i>Automatica</i>, vol. 156, p. Article 111204, 2023, doi: <a href=\"https://doi.org/doi: 10.1016/j.automatica.2023.111204 (open access)\">doi: 10.1016/j.automatica.2023.111204 (open access)</a>.","apa":"Lee, J. G., Berger, T., Trenn, S., &#38; Shim, H. (2023). Edge-wise funnel output synchronization of heterogeneous agents with relative degree one. <i>Automatica</i>, <i>156</i>, Article 111204. <a href=\"https://doi.org/doi: 10.1016/j.automatica.2023.111204 (open access)\">https://doi.org/doi: 10.1016/j.automatica.2023.111204 (open access)</a>","bibtex":"@article{Lee_Berger_Trenn_Shim_2023, title={Edge-wise funnel output synchronization of heterogeneous agents with relative degree one}, volume={156}, DOI={<a href=\"https://doi.org/doi: 10.1016/j.automatica.2023.111204 (open access)\">doi: 10.1016/j.automatica.2023.111204 (open access)</a>}, journal={Automatica}, author={Lee, J. G. and Berger, Thomas and Trenn, S. and Shim, H.}, year={2023}, pages={Article 111204} }","short":"J.G. Lee, T. Berger, S. Trenn, H. Shim, Automatica 156 (2023) Article 111204.","mla":"Lee, J. G., et al. “Edge-Wise Funnel Output Synchronization of Heterogeneous Agents with Relative Degree One.” <i>Automatica</i>, vol. 156, 2023, p. Article 111204, doi:<a href=\"https://doi.org/doi: 10.1016/j.automatica.2023.111204 (open access)\">doi: 10.1016/j.automatica.2023.111204 (open access)</a>."},"year":"2023","language":[{"iso":"eng"}],"department":[{"_id":"618"}],"user_id":"77457","_id":"53143","status":"public","publication":"Automatica","type":"journal_article"},{"title":"Uniqueness of the Inverse First Passage Time Problem and the Shape of the Shiryaev boundary","publisher":"Society for Industrial and Applied Mathematics","date_updated":"2023-01-10T08:13:30Z","date_created":"2023-01-10T08:13:17Z","author":[{"first_name":"Martin","full_name":"Kolb, Martin","id":"48880","last_name":"Kolb"},{"full_name":"Klump, Alexander","id":"45067","last_name":"Klump","first_name":"Alexander"}],"volume":67,"year":"2022","citation":{"ieee":"M. Kolb and A. Klump, “Uniqueness of the Inverse First Passage Time Problem and the Shape of the Shiryaev boundary,” <i>Theory of Probability and its Applications</i>, vol. 67, no. 4, pp. 717–744, 2022.","chicago":"Kolb, Martin, and Alexander Klump. “Uniqueness of the Inverse First Passage Time Problem and the Shape of the Shiryaev Boundary.” <i>Theory of Probability and Its Applications</i> 67, no. 4 (2022): 717–44.","apa":"Kolb, M., &#38; Klump, A. (2022). Uniqueness of the Inverse First Passage Time Problem and the Shape of the Shiryaev boundary. <i>Theory of Probability and Its Applications</i>, <i>67</i>(4), 717–744.","ama":"Kolb M, Klump A. Uniqueness of the Inverse First Passage Time Problem and the Shape of the Shiryaev boundary. <i>Theory of Probability and its Applications</i>. 2022;67(4):717-744.","short":"M. Kolb, A. Klump, Theory of Probability and Its Applications 67 (2022) 717–744.","bibtex":"@article{Kolb_Klump_2022, title={Uniqueness of the Inverse First Passage Time Problem and the Shape of the Shiryaev boundary}, volume={67}, number={4}, journal={Theory of Probability and its Applications}, publisher={Society for Industrial and Applied Mathematics}, author={Kolb, Martin and Klump, Alexander}, year={2022}, pages={717–744} }","mla":"Kolb, Martin, and Alexander Klump. “Uniqueness of the Inverse First Passage Time Problem and the Shape of the Shiryaev Boundary.” <i>Theory of Probability and Its Applications</i>, vol. 67, no. 4, Society for Industrial and Applied Mathematics, 2022, pp. 717–44."},"page":"717-744","intvolume":"        67","publication_status":"published","issue":"4","language":[{"iso":"eng"}],"_id":"35644","user_id":"85821","department":[{"_id":"96"}],"status":"public","type":"journal_article","publication":"Theory of Probability and its Applications"},{"language":[{"iso":"eng"}],"user_id":"85821","department":[{"_id":"96"}],"_id":"35649","status":"public","abstract":[{"text":"Motivated by the work [6] of Mariusz Bieniek, Krzysztof Burdzy and Soumik Pal we study a Fleming-Viot-type particle system consisting of independently moving particles each driven by generalized Bessel processes on the positive real line. Upon hitting the boundary {0} this particle is killed and an uniformly chosen different one branches into two particles. Using the symmetry of the model and the self similarity property of Bessel processes, we obtain a criterion to decide whether the particles converge to the origin at a finite time. This addresses open problem 1.4 in [6]. Specifically, inspired by [6, Open Problem 1.5], we investigate the case of three moving particles and refine the general result of [6, Theorem 1.1(ii)] extending the regime of drift parameters, where convergence does not occur – even to values, where it does occur when considering the case of only two particles.","lang":"eng"}],"type":"journal_article","publication":"Electronic Journal of Probability","doi":"https://doi.org/10.1214/22-EJP866","title":"On non-extinction in a Fleming-Viot-type particle model with Bessel drift","author":[{"first_name":"Martin","id":"48880","full_name":"Kolb, Martin","last_name":"Kolb"},{"last_name":"Liesenfeld","full_name":"Liesenfeld, Matthias","first_name":"Matthias"}],"date_created":"2023-01-10T08:19:25Z","publisher":"Institute of Mathematical Statistics","date_updated":"2023-01-10T08:19:38Z","citation":{"ieee":"M. Kolb and M. Liesenfeld, “On non-extinction in a Fleming-Viot-type particle model with Bessel drift,” <i>Electronic Journal of Probability</i>, no. 27, pp. 1–28, 2022, doi: <a href=\"https://doi.org/10.1214/22-EJP866\">https://doi.org/10.1214/22-EJP866</a>.","chicago":"Kolb, Martin, and Matthias Liesenfeld. “On Non-Extinction in a Fleming-Viot-Type Particle Model with Bessel Drift.” <i>Electronic Journal of Probability</i>, no. 27 (2022): 1–28. <a href=\"https://doi.org/10.1214/22-EJP866\">https://doi.org/10.1214/22-EJP866</a>.","ama":"Kolb M, Liesenfeld M. On non-extinction in a Fleming-Viot-type particle model with Bessel drift. <i>Electronic Journal of Probability</i>. 2022;(27):1-28. doi:<a href=\"https://doi.org/10.1214/22-EJP866\">https://doi.org/10.1214/22-EJP866</a>","apa":"Kolb, M., &#38; Liesenfeld, M. (2022). On non-extinction in a Fleming-Viot-type particle model with Bessel drift. <i>Electronic Journal of Probability</i>, <i>27</i>, 1–28. <a href=\"https://doi.org/10.1214/22-EJP866\">https://doi.org/10.1214/22-EJP866</a>","short":"M. Kolb, M. Liesenfeld, Electronic Journal of Probability (2022) 1–28.","bibtex":"@article{Kolb_Liesenfeld_2022, title={On non-extinction in a Fleming-Viot-type particle model with Bessel drift}, DOI={<a href=\"https://doi.org/10.1214/22-EJP866\">https://doi.org/10.1214/22-EJP866</a>}, number={27}, journal={Electronic Journal of Probability}, publisher={Institute of Mathematical Statistics}, author={Kolb, Martin and Liesenfeld, Matthias}, year={2022}, pages={1–28} }","mla":"Kolb, Martin, and Matthias Liesenfeld. “On Non-Extinction in a Fleming-Viot-Type Particle Model with Bessel Drift.” <i>Electronic Journal of Probability</i>, no. 27, Institute of Mathematical Statistics, 2022, pp. 1–28, doi:<a href=\"https://doi.org/10.1214/22-EJP866\">https://doi.org/10.1214/22-EJP866</a>."},"page":"1-28","year":"2022","issue":"27","publication_status":"published"},{"doi":"https://doi.org/10.48550/arXiv.2203.14772","title":"Persistence of autoregressive sequences with logarithmic tails","author":[{"first_name":"Denis","last_name":"Denisov","full_name":"Denisov, Denis"},{"full_name":"Hinrichs, Günter","last_name":"Hinrichs","first_name":"Günter"},{"first_name":"Martin","last_name":"Kolb","id":"48880","full_name":"Kolb, Martin"},{"first_name":"Vitali","full_name":"Wachtel, Vitali","last_name":"Wachtel"}],"date_created":"2023-01-10T08:28:12Z","volume":27,"publisher":"Institute of Mathematical Statistics","date_updated":"2023-01-10T08:29:02Z","citation":{"apa":"Denisov, D., Hinrichs, G., Kolb, M., &#38; Wachtel, V. (2022). Persistence of autoregressive sequences with logarithmic tails. <i>Electronic Journal of Probability</i>, <i>27</i>, 1–43. <a href=\"https://doi.org/10.48550/arXiv.2203.14772\">https://doi.org/10.48550/arXiv.2203.14772</a>","bibtex":"@article{Denisov_Hinrichs_Kolb_Wachtel_2022, title={Persistence of autoregressive sequences with logarithmic tails}, volume={27}, DOI={<a href=\"https://doi.org/10.48550/arXiv.2203.14772\">https://doi.org/10.48550/arXiv.2203.14772</a>}, journal={Electronic Journal of Probability}, publisher={Institute of Mathematical Statistics}, author={Denisov, Denis and Hinrichs, Günter and Kolb, Martin and Wachtel, Vitali}, year={2022}, pages={1–43} }","mla":"Denisov, Denis, et al. “Persistence of Autoregressive Sequences with Logarithmic Tails.” <i>Electronic Journal of Probability</i>, vol. 27, Institute of Mathematical Statistics, 2022, pp. 1–43, doi:<a href=\"https://doi.org/10.48550/arXiv.2203.14772\">https://doi.org/10.48550/arXiv.2203.14772</a>.","short":"D. Denisov, G. Hinrichs, M. Kolb, V. Wachtel, Electronic Journal of Probability 27 (2022) 1–43.","ama":"Denisov D, Hinrichs G, Kolb M, Wachtel V. Persistence of autoregressive sequences with logarithmic tails. <i>Electronic Journal of Probability</i>. 2022;27:1-43. doi:<a href=\"https://doi.org/10.48550/arXiv.2203.14772\">https://doi.org/10.48550/arXiv.2203.14772</a>","ieee":"D. Denisov, G. Hinrichs, M. Kolb, and V. Wachtel, “Persistence of autoregressive sequences with logarithmic tails,” <i>Electronic Journal of Probability</i>, vol. 27, pp. 1–43, 2022, doi: <a href=\"https://doi.org/10.48550/arXiv.2203.14772\">https://doi.org/10.48550/arXiv.2203.14772</a>.","chicago":"Denisov, Denis, Günter Hinrichs, Martin Kolb, and Vitali Wachtel. “Persistence of Autoregressive Sequences with Logarithmic Tails.” <i>Electronic Journal of Probability</i> 27 (2022): 1–43. <a href=\"https://doi.org/10.48550/arXiv.2203.14772\">https://doi.org/10.48550/arXiv.2203.14772</a>."},"intvolume":"        27","page":"1-43","year":"2022","publication_status":"published","language":[{"iso":"eng"}],"user_id":"85821","department":[{"_id":"96"}],"_id":"35650","status":"public","abstract":[{"text":"We consider autoregressive sequences Xn = aXn−1 + ξn and\r\nMn = max{aMn−1 , ξn} with a constant a ∈ (0, 1) and with positive, in-\r\ndependent and identically distributed innovations {ξk }. It is known that if\r\nP(ξ1 > x) ∼ d\r\nlog x with some d ∈ (0, − log a) then the chains {Xn} and {Mn}\r\nare null recurrent. We investigate the tail behaviour of recurrence times in this\r\ncase of logarithmically decaying tails. More precisely, we show that the tails\r\nof recurrence times are regularly varying of index −1 − d/ log a. We also prove\r\nlimit theorems for {Xn} and {Mn} conditioned to stay over a fixed level x0.\r\nFurthermore, we study tail asymptotics for recurrence times of {Xn} and {Mn}\r\nin the case when these chains are positive recurrent and the tail of log ξ1 is\r\nsubexponential.","lang":"eng"}],"type":"journal_article","publication":"Electronic Journal of Probability"},{"publication":"Annales Henri Poincaré ","abstract":[{"lang":"eng","text":"The kinetic Brownian motion on the sphere bundle of a Riemannian manifold M is a stochastic process that models a random perturbation of the geodesic flow. If M is an orientable compact constantly curved surface, we show that in the limit of infinitely large perturbation the L2-spectrum of the infinitesimal generator of a time-rescaled version of the process converges to the Laplace spectrum of the base manifold."}],"language":[{"iso":"eng"}],"issue":"4","year":"2021","publisher":"Springer Science + Business Media","date_created":"2022-09-07T07:05:33Z","title":"Spectral Asymptotics for Kinetic Brownian Motion on Surfaces of Constant Curvature","type":"journal_article","status":"public","_id":"33278","user_id":"85821","department":[{"_id":"96"}],"publication_status":"published","related_material":{"link":[{"relation":"contains","url":"https://link.springer.com/article/10.1007/s00023-021-01121-5"}]},"citation":{"ieee":"M. Kolb, T. Weich, and L. Wolf, “Spectral Asymptotics for Kinetic Brownian Motion on Surfaces of Constant Curvature,” <i>Annales Henri Poincaré </i>, vol. 23, no. 4, pp. 1283–1296, 2021.","chicago":"Kolb, Martin, Tobias Weich, and Lasse Wolf. “Spectral Asymptotics for Kinetic Brownian Motion on Surfaces of Constant Curvature.” <i>Annales Henri Poincaré </i> 23, no. 4 (2021): 1283–96.","ama":"Kolb M, Weich T, Wolf L. Spectral Asymptotics for Kinetic Brownian Motion on Surfaces of Constant Curvature. <i>Annales Henri Poincaré </i>. 2021;23(4):1283-1296.","apa":"Kolb, M., Weich, T., &#38; Wolf, L. (2021). Spectral Asymptotics for Kinetic Brownian Motion on Surfaces of Constant Curvature. <i>Annales Henri Poincaré </i>, <i>23</i>(4), 1283–1296.","mla":"Kolb, Martin, et al. “Spectral Asymptotics for Kinetic Brownian Motion on Surfaces of Constant Curvature.” <i>Annales Henri Poincaré </i>, vol. 23, no. 4, Springer Science + Business Media, 2021, pp. 1283–96.","short":"M. Kolb, T. Weich, L. Wolf, Annales Henri Poincaré  23 (2021) 1283–1296.","bibtex":"@article{Kolb_Weich_Wolf_2021, title={Spectral Asymptotics for Kinetic Brownian Motion on Surfaces of Constant Curvature}, volume={23}, number={4}, journal={Annales Henri Poincaré }, publisher={Springer Science + Business Media}, author={Kolb, Martin and Weich, Tobias and Wolf, Lasse}, year={2021}, pages={1283–1296} }"},"intvolume":"        23","page":"1283-1296","oa":"1","date_updated":"2022-09-08T06:06:13Z","author":[{"first_name":"Martin","last_name":"Kolb","id":"48880","full_name":"Kolb, Martin"},{"last_name":"Weich","full_name":"Weich, Tobias","first_name":"Tobias"},{"full_name":"Wolf, Lasse","last_name":"Wolf","first_name":"Lasse"}],"volume":23,"main_file_link":[{"url":"https://link.springer.com/article/10.1007/s00023-021-01121-5","open_access":"1"}]},{"language":[{"iso":"eng"}],"department":[{"_id":"96"}],"user_id":"85821","_id":"33481","status":"public","abstract":[{"text":"While 2D Gibbsian particle systems might exhibit orientational order resulting in a lattice-like structure, these particle systems do not exhibit positional order if the interaction between particles satisfies some weak assumptions. Here we investigate to which extent particles within a box of size may fluctuate from their ideal lattice position. We show that particles near the center of the box typically show a displacement at least of order . Thus we extend recent results on the hard disk model to particle systems with fairly arbitrary particle spins and interaction. Our result applies to models such as rather general continuum Potts type models, e.g. with Widom–Rowlinson or Lenard-Jones-type interaction.","lang":"eng"}],"publication":"Stochastic Processes and their Applications","type":"journal_article","doi":"https://doi.org/10.1016/j.spa.2020.10.003","title":"A lower bound on the displacement of particles in 2D Gibbsian particle systems","volume":132,"author":[{"first_name":"Thomas","last_name":"Richthammer","id":"62054","full_name":"Richthammer, Thomas"},{"last_name":"Fiedler","full_name":"Fiedler, Michael","first_name":"Michael"}],"date_created":"2022-09-26T06:53:59Z","date_updated":"2022-09-26T06:54:06Z","publisher":"Elsevier","page":"1-32","intvolume":"       132","citation":{"short":"T. Richthammer, M. Fiedler, Stochastic Processes and Their Applications 132 (2021) 1–32.","mla":"Richthammer, Thomas, and Michael Fiedler. “A Lower Bound on the Displacement of Particles in 2D Gibbsian Particle Systems.” <i>Stochastic Processes and Their Applications</i>, vol. 132, Elsevier, 2021, pp. 1–32, doi:<a href=\"https://doi.org/10.1016/j.spa.2020.10.003\">https://doi.org/10.1016/j.spa.2020.10.003</a>.","bibtex":"@article{Richthammer_Fiedler_2021, title={A lower bound on the displacement of particles in 2D Gibbsian particle systems}, volume={132}, DOI={<a href=\"https://doi.org/10.1016/j.spa.2020.10.003\">https://doi.org/10.1016/j.spa.2020.10.003</a>}, journal={Stochastic Processes and their Applications}, publisher={Elsevier}, author={Richthammer, Thomas and Fiedler, Michael}, year={2021}, pages={1–32} }","apa":"Richthammer, T., &#38; Fiedler, M. (2021). A lower bound on the displacement of particles in 2D Gibbsian particle systems. <i>Stochastic Processes and Their Applications</i>, <i>132</i>, 1–32. <a href=\"https://doi.org/10.1016/j.spa.2020.10.003\">https://doi.org/10.1016/j.spa.2020.10.003</a>","chicago":"Richthammer, Thomas, and Michael Fiedler. “A Lower Bound on the Displacement of Particles in 2D Gibbsian Particle Systems.” <i>Stochastic Processes and Their Applications</i> 132 (2021): 1–32. <a href=\"https://doi.org/10.1016/j.spa.2020.10.003\">https://doi.org/10.1016/j.spa.2020.10.003</a>.","ieee":"T. Richthammer and M. Fiedler, “A lower bound on the displacement of particles in 2D Gibbsian particle systems,” <i>Stochastic Processes and their Applications</i>, vol. 132, pp. 1–32, 2021, doi: <a href=\"https://doi.org/10.1016/j.spa.2020.10.003\">https://doi.org/10.1016/j.spa.2020.10.003</a>.","ama":"Richthammer T, Fiedler M. A lower bound on the displacement of particles in 2D Gibbsian particle systems. <i>Stochastic Processes and their Applications</i>. 2021;132:1-32. doi:<a href=\"https://doi.org/10.1016/j.spa.2020.10.003\">https://doi.org/10.1016/j.spa.2020.10.003</a>"},"year":"2021","publication_status":"published"},{"type":"misc","status":"public","abstract":[{"lang":"ger","text":"Dieses Lernangebot widmet sich der linearen Algebra als dem Teil der Mathematik, der neben der Optimierung und der Stochastik die Grundlage für praktisch alle Entwicklungen im Bereich Künstliche Intelligenz (KI) darstellt. Das Fach ist jedoch für Anfänger meist ungewohnt abstrakt und wird daher oft als besonders schwierig und unanschaulich empfunden. In diesem Kurs wird das Erlernen mathematischer Kenntnisse in linearer Algebra verknüpft mit dem aktuellen und faszinierenden Anwendungsfeld der künstlichen neuronalen Netze (KNN). Daraus ergeben sich in natürlicher Weise Anwendungsbeispiele, an denen die wesentlichen Konzepte der linearen Algebra erklärt werden können.\r\n\r\nBehandelte Themen sind:\r\n\r\n    Der Vektorraum der reellen Zahlentupel, reelle Vektorräume allgemein\r\n    Lineare Abbildungen\r\n    Matrizen\r\n    Koordinaten und darstellende Matrizen\r\n    Lineare Gleichungssysteme, Gaußalgorithmus\r\n    Determinante\r\n    Ein Ausblick auf nichtlineare Techniken, die für neuronale Netzwerke relevant sind."}],"user_id":"97359","department":[{"_id":"94"}],"_id":"33273","language":[{"iso":"eng"}],"extern":"1","citation":{"chicago":"Schramm, Thomas, Ingenuin Gasser, Sören Schwenker, Ruedi Seiler, Alexander Lohse, and Kay Zobel. <i>Linear Algebra Driven by Data Science</i>. Hamburg Open Online University, 2020.","ieee":"T. Schramm, I. Gasser, S. Schwenker, R. Seiler, A. Lohse, and K. Zobel, <i>Linear Algebra driven by Data Science</i>. Hamburg Open Online University, 2020.","ama":"Schramm T, Gasser I, Schwenker S, Seiler R, Lohse A, Zobel K. <i>Linear Algebra Driven by Data Science</i>. Hamburg Open Online University; 2020.","apa":"Schramm, T., Gasser, I., Schwenker, S., Seiler, R., Lohse, A., &#38; Zobel, K. (2020). <i>Linear Algebra driven by Data Science</i>. Hamburg Open Online University.","bibtex":"@book{Schramm_Gasser_Schwenker_Seiler_Lohse_Zobel_2020, title={Linear Algebra driven by Data Science}, publisher={Hamburg Open Online University}, author={Schramm, Thomas and Gasser, Ingenuin and Schwenker, Sören and Seiler, Ruedi and Lohse, Alexander and Zobel, Kay}, year={2020} }","mla":"Schramm, Thomas, et al. <i>Linear Algebra Driven by Data Science</i>. Hamburg Open Online University, 2020.","short":"T. Schramm, I. Gasser, S. Schwenker, R. Seiler, A. Lohse, K. Zobel, Linear Algebra Driven by Data Science, Hamburg Open Online University, 2020."},"year":"2020","date_created":"2022-09-06T12:06:41Z","author":[{"last_name":"Schramm","full_name":"Schramm, Thomas","first_name":"Thomas"},{"last_name":"Gasser","full_name":"Gasser, Ingenuin","first_name":"Ingenuin"},{"last_name":"Schwenker","orcid":"0000-0002-8054-2058","id":"97359","full_name":"Schwenker, Sören","first_name":"Sören"},{"first_name":"Ruedi","last_name":"Seiler","full_name":"Seiler, Ruedi"},{"first_name":"Alexander","full_name":"Lohse, Alexander","last_name":"Lohse"},{"first_name":"Kay","full_name":"Zobel, Kay","last_name":"Zobel"}],"publisher":"Hamburg Open Online University","date_updated":"2022-09-06T14:05:13Z","main_file_link":[{"url":"https://www.hoou.de/projects/linear-algebra-driven-by-data-science/"}],"title":"Linear Algebra driven by Data Science"},{"type":"journal_article","publication":"Bernoulli","status":"public","abstract":[{"text":"We derive a criterium for the almost sure finiteness of perpetual integrals of L ́evy\r\nprocesses for a class of real functions including all continuous functions and for general one-\r\ndimensional L ́evy processes that drifts to plus infinity. This generalizes previous work of D ̈oring\r\nand Kyprianou, who considered L ́evy processes having a local time, leaving the general case as an\r\nopen problem. It turns out, that the criterium in the general situation simplifies significantly in\r\nthe situation, where the process has a local time, but we also demonstrate that in general our cri-\r\nterium can not be reduced. This answers an open problem posed in D ̈oring, L. and Kyprianou, A.\r\n(2015).","lang":"eng"}],"user_id":"85821","department":[{"_id":"96"}],"_id":"33282","language":[{"iso":"eng"}],"keyword":["L ́evy processes","Perpetual integrals","Potential measures"],"issue":"2","publication_status":"published","citation":{"ieee":"M. Kolb and M. Savov, “A Characterization of the Finiteness of Perpetual Integrals of Levy Processes,” <i>Bernoulli</i>, vol. 26, no. 2, pp. 1453–1472, 2020, doi: <a href=\"https://doi.org/10.48550/arXiv.1903.03792\">https://doi.org/10.48550/arXiv.1903.03792</a>.","chicago":"Kolb, Martin, and Mladen Savov. “A Characterization of the Finiteness of Perpetual Integrals of Levy Processes.” <i>Bernoulli</i> 26, no. 2 (2020): 1453–72. <a href=\"https://doi.org/10.48550/arXiv.1903.03792\">https://doi.org/10.48550/arXiv.1903.03792</a>.","ama":"Kolb M, Savov M. A Characterization of the Finiteness of Perpetual Integrals of Levy Processes. <i>Bernoulli</i>. 2020;26(2):1453-1472. doi:<a href=\"https://doi.org/10.48550/arXiv.1903.03792\">https://doi.org/10.48550/arXiv.1903.03792</a>","apa":"Kolb, M., &#38; Savov, M. (2020). A Characterization of the Finiteness of Perpetual Integrals of Levy Processes. <i>Bernoulli</i>, <i>26</i>(2), 1453–1472. <a href=\"https://doi.org/10.48550/arXiv.1903.03792\">https://doi.org/10.48550/arXiv.1903.03792</a>","bibtex":"@article{Kolb_Savov_2020, title={A Characterization of the Finiteness of Perpetual Integrals of Levy Processes}, volume={26}, DOI={<a href=\"https://doi.org/10.48550/arXiv.1903.03792\">https://doi.org/10.48550/arXiv.1903.03792</a>}, number={2}, journal={Bernoulli}, publisher={Bernoulli Society for Mathematical Statistics and Probability}, author={Kolb, Martin and Savov, Mladen}, year={2020}, pages={1453–1472} }","short":"M. Kolb, M. Savov, Bernoulli 26 (2020) 1453–1472.","mla":"Kolb, Martin, and Mladen Savov. “A Characterization of the Finiteness of Perpetual Integrals of Levy Processes.” <i>Bernoulli</i>, vol. 26, no. 2, Bernoulli Society for Mathematical Statistics and Probability, 2020, pp. 1453–72, doi:<a href=\"https://doi.org/10.48550/arXiv.1903.03792\">https://doi.org/10.48550/arXiv.1903.03792</a>."},"intvolume":"        26","page":"1453-1472","year":"2020","author":[{"full_name":"Kolb, Martin","id":"48880","last_name":"Kolb","first_name":"Martin"},{"last_name":"Savov","full_name":"Savov, Mladen","first_name":"Mladen"}],"date_created":"2022-09-08T06:36:37Z","volume":26,"publisher":"Bernoulli Society for Mathematical Statistics and Probability","date_updated":"2022-09-08T06:48:40Z","doi":"https://doi.org/10.48550/arXiv.1903.03792","title":"A Characterization of the Finiteness of Perpetual Integrals of Levy Processes"},{"language":[{"iso":"eng"}],"_id":"33330","user_id":"85821","department":[{"_id":"96"}],"abstract":[{"lang":"eng","text":"Reciprocal relations are binary relations Q with entries Q(i,j)∈[0,1], and such that Q(i,j)+Q(j,i)=1. Relations of this kind occur quite naturally in various domains, such as preference modeling and preference learning. For example, Q(i,j) could be the fraction of voters in a population who prefer candidate i to candidate j. In the literature, various attempts have been made at generalizing the notion of transitivity to reciprocal relations. In this paper, we compare three important frameworks of generalized transitivity: g-stochastic transitivity, T-transitivity, and cycle-transitivity. To this end, we introduce E-transitivity as an even more general notion. We also use this framework to extend an existing hierarchy of different types of transitivity. As an illustration, we study transitivity properties of probabilities of pairwise preferences, which are induced as marginals of an underlying probability distribution on rankings (strict total orders) of a set of alternatives. In particular, we analyze the interesting case of the so-called Babington Smith model, a parametric family of distributions of that kind."}],"status":"public","type":"journal_article","publication":"International Journal of Approximate Reasoning","title":"Generalized transitivity: A systematic comparison of concepts with an application to preferences in the Babington Smith model","doi":"https://doi.org/10.1016/j.ijar.2020.01.007","date_updated":"2022-09-12T07:13:30Z","publisher":"Elsevier","date_created":"2022-09-12T07:13:19Z","author":[{"first_name":"Björn","last_name":"Haddenhorst","full_name":"Haddenhorst, Björn"},{"full_name":"Hüllermeier, Eyke","last_name":"Hüllermeier","first_name":"Eyke"},{"first_name":"Martin","id":"48880","full_name":"Kolb, Martin","last_name":"Kolb"}],"volume":119,"year":"2020","citation":{"bibtex":"@article{Haddenhorst_Hüllermeier_Kolb_2020, title={Generalized transitivity: A systematic comparison of concepts with an application to preferences in the Babington Smith model}, volume={119}, DOI={<a href=\"https://doi.org/10.1016/j.ijar.2020.01.007\">https://doi.org/10.1016/j.ijar.2020.01.007</a>}, number={2}, journal={International Journal of Approximate Reasoning}, publisher={Elsevier}, author={Haddenhorst, Björn and Hüllermeier, Eyke and Kolb, Martin}, year={2020}, pages={373–407} }","mla":"Haddenhorst, Björn, et al. “Generalized Transitivity: A Systematic Comparison of Concepts with an Application to Preferences in the Babington Smith Model.” <i>International Journal of Approximate Reasoning</i>, vol. 119, no. 2, Elsevier, 2020, pp. 373–407, doi:<a href=\"https://doi.org/10.1016/j.ijar.2020.01.007\">https://doi.org/10.1016/j.ijar.2020.01.007</a>.","short":"B. Haddenhorst, E. Hüllermeier, M. Kolb, International Journal of Approximate Reasoning 119 (2020) 373–407.","apa":"Haddenhorst, B., Hüllermeier, E., &#38; Kolb, M. (2020). Generalized transitivity: A systematic comparison of concepts with an application to preferences in the Babington Smith model. <i>International Journal of Approximate Reasoning</i>, <i>119</i>(2), 373–407. <a href=\"https://doi.org/10.1016/j.ijar.2020.01.007\">https://doi.org/10.1016/j.ijar.2020.01.007</a>","ama":"Haddenhorst B, Hüllermeier E, Kolb M. Generalized transitivity: A systematic comparison of concepts with an application to preferences in the Babington Smith model. <i>International Journal of Approximate Reasoning</i>. 2020;119(2):373-407. doi:<a href=\"https://doi.org/10.1016/j.ijar.2020.01.007\">https://doi.org/10.1016/j.ijar.2020.01.007</a>","chicago":"Haddenhorst, Björn, Eyke Hüllermeier, and Martin Kolb. “Generalized Transitivity: A Systematic Comparison of Concepts with an Application to Preferences in the Babington Smith Model.” <i>International Journal of Approximate Reasoning</i> 119, no. 2 (2020): 373–407. <a href=\"https://doi.org/10.1016/j.ijar.2020.01.007\">https://doi.org/10.1016/j.ijar.2020.01.007</a>.","ieee":"B. Haddenhorst, E. Hüllermeier, and M. Kolb, “Generalized transitivity: A systematic comparison of concepts with an application to preferences in the Babington Smith model,” <i>International Journal of Approximate Reasoning</i>, vol. 119, no. 2, pp. 373–407, 2020, doi: <a href=\"https://doi.org/10.1016/j.ijar.2020.01.007\">https://doi.org/10.1016/j.ijar.2020.01.007</a>."},"page":"373-407","intvolume":"       119","publication_status":"published","issue":"2"},{"abstract":[{"text":"Motivated by the recent contribution (Bauer and Bernard in Annales Henri Poincaré 19:653–693, 2018), we study the scaling limit behavior of a class of one-dimensional stochastic differential equations which has a unique attracting point subject to a small additional repulsive perturbation. Problems of this type appear in the analysis of continuously monitored quantum systems. We extend the results of Bauer and Bernard (Annales Henri Poincaré 19:653–693, 2018) and prove a general result concerning the convergence to a homogeneous Poisson process using only classical probabilistic tools.","lang":"eng"}],"status":"public","type":"journal_article","publication":"Annales Henri Poincaré","language":[{"iso":"eng"}],"_id":"33331","user_id":"85821","department":[{"_id":"96"}],"year":"2019","citation":{"short":"M. Kolb, M. Liesenfeld, Annales Henri Poincaré 20 (2019) 1753–1783.","bibtex":"@article{Kolb_Liesenfeld_2019, title={Stochastic Spikes and Poisson Approximation of One-Dimensional Stochastic Differential Equations with Applications to Continuously Measured Quantum Systems}, volume={20}, DOI={<a href=\"http://dx.doi.org/10.1007/s00023-019-00772-9\">http://dx.doi.org/10.1007/s00023-019-00772-9</a>}, number={6}, journal={Annales Henri Poincaré}, publisher={Institute Henri Poincaré}, author={Kolb, Martin and Liesenfeld, Matthias}, year={2019}, pages={1753–1783} }","mla":"Kolb, Martin, and Matthias Liesenfeld. “Stochastic Spikes and Poisson Approximation of One-Dimensional Stochastic Differential Equations with Applications to Continuously Measured Quantum Systems.” <i>Annales Henri Poincaré</i>, vol. 20, no. 6, Institute Henri Poincaré, 2019, pp. 1753–83, doi:<a href=\"http://dx.doi.org/10.1007/s00023-019-00772-9\">http://dx.doi.org/10.1007/s00023-019-00772-9</a>.","apa":"Kolb, M., &#38; Liesenfeld, M. (2019). Stochastic Spikes and Poisson Approximation of One-Dimensional Stochastic Differential Equations with Applications to Continuously Measured Quantum Systems. <i>Annales Henri Poincaré</i>, <i>20</i>(6), 1753–1783. <a href=\"http://dx.doi.org/10.1007/s00023-019-00772-9\">http://dx.doi.org/10.1007/s00023-019-00772-9</a>","ama":"Kolb M, Liesenfeld M. Stochastic Spikes and Poisson Approximation of One-Dimensional Stochastic Differential Equations with Applications to Continuously Measured Quantum Systems. <i>Annales Henri Poincaré</i>. 2019;20(6):1753-1783. doi:<a href=\"http://dx.doi.org/10.1007/s00023-019-00772-9\">http://dx.doi.org/10.1007/s00023-019-00772-9</a>","chicago":"Kolb, Martin, and Matthias Liesenfeld. “Stochastic Spikes and Poisson Approximation of One-Dimensional Stochastic Differential Equations with Applications to Continuously Measured Quantum Systems.” <i>Annales Henri Poincaré</i> 20, no. 6 (2019): 1753–83. <a href=\"http://dx.doi.org/10.1007/s00023-019-00772-9\">http://dx.doi.org/10.1007/s00023-019-00772-9</a>.","ieee":"M. Kolb and M. Liesenfeld, “Stochastic Spikes and Poisson Approximation of One-Dimensional Stochastic Differential Equations with Applications to Continuously Measured Quantum Systems,” <i>Annales Henri Poincaré</i>, vol. 20, no. 6, pp. 1753–1783, 2019, doi: <a href=\"http://dx.doi.org/10.1007/s00023-019-00772-9\">http://dx.doi.org/10.1007/s00023-019-00772-9</a>."},"page":"1753-1783","intvolume":"        20","publication_status":"published","issue":"6","title":"Stochastic Spikes and Poisson Approximation of One-Dimensional Stochastic Differential Equations with Applications to Continuously Measured Quantum Systems","doi":"http://dx.doi.org/10.1007/s00023-019-00772-9","publisher":"Institute Henri Poincaré","date_updated":"2022-09-12T07:19:02Z","author":[{"full_name":"Kolb, Martin","id":"48880","last_name":"Kolb","first_name":"Martin"},{"first_name":"Matthias","full_name":"Liesenfeld, Matthias","last_name":"Liesenfeld"}],"date_created":"2022-09-12T07:18:58Z","volume":20}]