[{"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","type":"preprint","publication":"arXiv:2603.01994","language":[{"iso":"eng"}],"external_id":{"arxiv":["2603.01994"]},"_id":"64816","user_id":"113768","department":[{"_id":"94"}],"year":"2026","citation":{"apa":"Jalowy, J., Lammers, I., &#38; Löwe, M. (2026). The infinite block spin Ising model. In <i>arXiv:2603.01994</i>.","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.","ieee":"J. Jalowy, I. Lammers, and M. Löwe, “The infinite block spin Ising model,” <i>arXiv:2603.01994</i>. 2026.","chicago":"Jalowy, Jonas, Isabel Lammers, and Matthias Löwe. “The Infinite Block Spin Ising Model.” <i>ArXiv:2603.01994</i>, 2026.","ama":"Jalowy J, Lammers I, Löwe M. The infinite block spin Ising model. <i>arXiv:260301994</i>. Published online 2026."},"title":"The infinite block spin Ising model","date_updated":"2026-03-03T08:49:33Z","author":[{"orcid":"0000-0001-9624-2685","last_name":"Jalowy","full_name":"Jalowy, Jonas","id":"113768","first_name":"Jonas"},{"last_name":"Lammers","full_name":"Lammers, Isabel","first_name":"Isabel"},{"first_name":"Matthias","last_name":"Löwe","full_name":"Löwe, Matthias"}],"date_created":"2026-03-03T08:49:16Z"},{"citation":{"short":"J. Jalowy, Z. Kabluchko, A. Marynych, ArXiv:2504.11593 (2025).","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} }","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>.","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.","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.","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."},"year":"2025","date_created":"2025-04-23T14:37:41Z","author":[{"id":"113768","full_name":"Jalowy, Jonas","orcid":"0000-0001-9624-2685","last_name":"Jalowy","first_name":"Jonas"},{"last_name":"Kabluchko","full_name":"Kabluchko, Zakhar","first_name":"Zakhar"},{"first_name":"Alexander","full_name":"Marynych, Alexander","last_name":"Marynych"}],"date_updated":"2025-04-23T14:38:04Z","title":"Zeros and exponential profiles of polynomials I: Limit distributions,  finite free convolutions and repeated differentiation","type":"preprint","publication":"arXiv:2504.11593","status":"public","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"}],"user_id":"113768","department":[{"_id":"94"}],"_id":"59664","external_id":{"arxiv":["2504.11593"]},"language":[{"iso":"eng"}]},{"year":"2025","citation":{"mla":"Jalowy, Jonas, et al. “Propagation of Chaos and Residual Dependence in Gibbs Measures on Finite Sets.” <i>Mathematical Physics, Analysis and Geometry</i>, vol. 28, no. 1, 6, Springer Science and Business Media LLC, 2025, doi:<a href=\"https://doi.org/10.1007/s11040-025-09503-5\">10.1007/s11040-025-09503-5</a>.","short":"J. Jalowy, Z. Kabluchko, M. Löwe, Mathematical Physics, Analysis and Geometry 28 (2025).","bibtex":"@article{Jalowy_Kabluchko_Löwe_2025, title={Propagation of Chaos and Residual Dependence in Gibbs Measures on Finite Sets}, volume={28}, DOI={<a href=\"https://doi.org/10.1007/s11040-025-09503-5\">10.1007/s11040-025-09503-5</a>}, number={16}, journal={Mathematical Physics, Analysis and Geometry}, publisher={Springer Science and Business Media LLC}, author={Jalowy, Jonas and Kabluchko, Zakhar and Löwe, Matthias}, year={2025} }","apa":"Jalowy, J., Kabluchko, Z., &#38; Löwe, M. (2025). Propagation of Chaos and Residual Dependence in Gibbs Measures on Finite Sets. <i>Mathematical Physics, Analysis and Geometry</i>, <i>28</i>(1), Article 6. <a href=\"https://doi.org/10.1007/s11040-025-09503-5\">https://doi.org/10.1007/s11040-025-09503-5</a>","ama":"Jalowy J, Kabluchko Z, Löwe M. Propagation of Chaos and Residual Dependence in Gibbs Measures on Finite Sets. <i>Mathematical Physics, Analysis and Geometry</i>. 2025;28(1). doi:<a href=\"https://doi.org/10.1007/s11040-025-09503-5\">10.1007/s11040-025-09503-5</a>","ieee":"J. Jalowy, Z. Kabluchko, and M. Löwe, “Propagation of Chaos and Residual Dependence in Gibbs Measures on Finite Sets,” <i>Mathematical Physics, Analysis and Geometry</i>, vol. 28, no. 1, Art. no. 6, 2025, doi: <a href=\"https://doi.org/10.1007/s11040-025-09503-5\">10.1007/s11040-025-09503-5</a>.","chicago":"Jalowy, Jonas, Zakhar Kabluchko, and Matthias Löwe. “Propagation of Chaos and Residual Dependence in Gibbs Measures on Finite Sets.” <i>Mathematical Physics, Analysis and Geometry</i> 28, no. 1 (2025). <a href=\"https://doi.org/10.1007/s11040-025-09503-5\">https://doi.org/10.1007/s11040-025-09503-5</a>."},"intvolume":"        28","publication_status":"published","publication_identifier":{"issn":["1385-0172","1572-9656"]},"issue":"1","title":"Propagation of Chaos and Residual Dependence in Gibbs Measures on Finite Sets","doi":"10.1007/s11040-025-09503-5","date_updated":"2025-04-23T14:39:12Z","publisher":"Springer Science and Business Media LLC","author":[{"last_name":"Jalowy","orcid":"0000-0001-9624-2685","id":"113768","full_name":"Jalowy, Jonas","first_name":"Jonas"},{"full_name":"Kabluchko, Zakhar","last_name":"Kabluchko","first_name":"Zakhar"},{"last_name":"Löwe","full_name":"Löwe, Matthias","first_name":"Matthias"}],"date_created":"2025-03-31T07:17:19Z","volume":28,"abstract":[{"lang":"eng","text":"<jats:title>Abstract</jats:title>\r\n          <jats:p>We compare a mean-field Gibbs distribution on a finite state space on <jats:italic>N</jats:italic> spins to that of an explicit simple mixture of product measures. This illustrates the situation beyond the so-called <jats:italic>increasing propagation of chaos</jats:italic> introduced by Ben Arous and Zeitouni [3], where marginal distributions of size <jats:inline-formula>\r\n              <jats:alternatives>\r\n                <jats:tex-math>$$k=o(N)$$</jats:tex-math>\r\n                <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                  <mml:mrow>\r\n                    <mml:mi>k</mml:mi>\r\n                    <mml:mo>=</mml:mo>\r\n                    <mml:mi>o</mml:mi>\r\n                    <mml:mo>(</mml:mo>\r\n                    <mml:mi>N</mml:mi>\r\n                    <mml:mo>)</mml:mo>\r\n                  </mml:mrow>\r\n                </mml:math>\r\n              </jats:alternatives>\r\n            </jats:inline-formula> are compared to product measures.</jats:p>"}],"status":"public","type":"journal_article","publication":"Mathematical Physics, Analysis and Geometry","article_number":"6","language":[{"iso":"eng"}],"_id":"59213","user_id":"113768"},{"issue":"4","publication_identifier":{"issn":["0022-1236"]},"publication_status":"published","intvolume":"       289","citation":{"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).","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>","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>."},"year":"2025","volume":289,"author":[{"last_name":"Erbar","full_name":"Erbar, Matthias","first_name":"Matthias"},{"first_name":"Martin","full_name":"Huesmann, Martin","last_name":"Huesmann"},{"full_name":"Jalowy, Jonas","id":"113768","last_name":"Jalowy","orcid":"0000-0001-9624-2685","first_name":"Jonas"},{"first_name":"Bastian","full_name":"Müller, Bastian","last_name":"Müller"}],"date_created":"2025-04-23T14:39:50Z","publisher":"Elsevier BV","date_updated":"2025-04-23T14:41:19Z","doi":"10.1016/j.jfa.2025.110974","title":"Optimal transport of stationary point processes: Metric structure, gradient flow and convexity of the specific entropy","publication":"Journal of Functional Analysis","type":"journal_article","status":"public","department":[{"_id":"94"}],"user_id":"113768","_id":"59665","language":[{"iso":"eng"}],"article_number":"110974"},{"citation":{"ama":"Jalowy J, Stange H. Box-Covariances of Hyperuniform Point Processes. <i>arXiv:250613661</i>. Published online 2025.","chicago":"Jalowy, Jonas, and Hanna Stange. “Box-Covariances of Hyperuniform Point Processes.” <i>ArXiv:2506.13661</i>, 2025.","ieee":"J. Jalowy and H. Stange, “Box-Covariances of Hyperuniform Point Processes,” <i>arXiv:2506.13661</i>. 2025.","short":"J. Jalowy, H. Stange, ArXiv:2506.13661 (2025).","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.","apa":"Jalowy, J., &#38; Stange, H. (2025). Box-Covariances of Hyperuniform Point Processes. In <i>arXiv:2506.13661</i>."},"year":"2025","title":"Box-Covariances of Hyperuniform Point Processes","author":[{"first_name":"Jonas","id":"113768","full_name":"Jalowy, Jonas","orcid":"0000-0001-9624-2685","last_name":"Jalowy"},{"last_name":"Stange","full_name":"Stange, Hanna","first_name":"Hanna"}],"date_created":"2025-06-22T08:02:28Z","date_updated":"2025-06-22T08:03:20Z","status":"public","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."}],"type":"preprint","publication":"arXiv:2506.13661","language":[{"iso":"eng"}],"user_id":"113768","department":[{"_id":"94"}],"external_id":{"arxiv":["2506.13661"]},"_id":"60293"},{"title":"Moderate-to-large deviation asymptotics for real eigenvalues of the elliptic Ginibre matrices","date_created":"2025-12-22T08:37:02Z","author":[{"first_name":"Sung-Soo","last_name":"Byun","full_name":"Byun, Sung-Soo"},{"orcid":"0000-0001-9624-2685","last_name":"Jalowy","id":"113768","full_name":"Jalowy, Jonas","first_name":"Jonas"},{"first_name":"Yong-Woo","last_name":"Lee","full_name":"Lee, Yong-Woo"},{"first_name":"Grégory","full_name":"Schehr, Grégory","last_name":"Schehr"}],"date_updated":"2025-12-22T08:37:35Z","citation":{"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.","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.","short":"S.-S. Byun, J. Jalowy, Y.-W. Lee, G. Schehr, ArXiv:2511.09191 (2025).","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} }","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.","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>."},"year":"2025","language":[{"iso":"eng"}],"user_id":"113768","department":[{"_id":"94"}],"external_id":{"arxiv":["2511.09191"]},"_id":"63394","status":"public","abstract":[{"lang":"eng","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."}],"type":"preprint","publication":"arXiv:2511.09191"},{"status":"public","abstract":[{"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.","lang":"eng"}],"type":"preprint","publication":"arXiv:2512.17808","language":[{"iso":"eng"}],"user_id":"113768","department":[{"_id":"94"}],"_id":"63393","external_id":{"arxiv":["2512.17808"]},"citation":{"chicago":"Höfert, Antonia, Jonas Jalowy, and Zakhar Kabluchko. “Zeros of Polynomial Powers under the Heat Flow.” <i>ArXiv:2512.17808</i>, 2025.","ieee":"A. Höfert, J. Jalowy, and Z. Kabluchko, “Zeros of polynomial powers under the heat flow,” <i>arXiv:2512.17808</i>. 2025.","ama":"Höfert A, Jalowy J, Kabluchko Z. Zeros of polynomial powers under the heat flow. <i>arXiv:251217808</i>. Published online 2025.","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>."},"year":"2025","title":"Zeros of polynomial powers under the heat flow","author":[{"last_name":"Höfert","full_name":"Höfert, Antonia","first_name":"Antonia"},{"full_name":"Jalowy, Jonas","id":"113768","last_name":"Jalowy","orcid":"0000-0001-9624-2685","first_name":"Jonas"},{"full_name":"Kabluchko, Zakhar","last_name":"Kabluchko","first_name":"Zakhar"}],"date_created":"2025-12-22T08:36:24Z","date_updated":"2025-12-22T08:36:46Z"},{"type":"journal_article","publication":"Electronic Journal of Probability","status":"public","user_id":"113768","_id":"59188","language":[{"iso":"eng"}],"issue":"none","publication_status":"published","publication_identifier":{"issn":["1083-6489"]},"citation":{"mla":"Jalowy, Jonas, et al. “When Does the Chaos in the Curie-Weiss Model Stop to Propagate?” <i>Electronic Journal of Probability</i>, vol. 28, no. none, Institute of Mathematical Statistics, 2023, doi:<a href=\"https://doi.org/10.1214/23-ejp1039\">10.1214/23-ejp1039</a>.","short":"J. Jalowy, Z. Kabluchko, M. Löwe, A. Marynych, Electronic Journal of Probability 28 (2023).","bibtex":"@article{Jalowy_Kabluchko_Löwe_Marynych_2023, title={When does the chaos in the Curie-Weiss model stop to propagate?}, volume={28}, DOI={<a href=\"https://doi.org/10.1214/23-ejp1039\">10.1214/23-ejp1039</a>}, number={none}, journal={Electronic Journal of Probability}, publisher={Institute of Mathematical Statistics}, author={Jalowy, Jonas and Kabluchko, Zakhar and Löwe, Matthias and Marynych, Alexander}, year={2023} }","apa":"Jalowy, J., Kabluchko, Z., Löwe, M., &#38; Marynych, A. (2023). When does the chaos in the Curie-Weiss model stop to propagate? <i>Electronic Journal of Probability</i>, <i>28</i>(none). <a href=\"https://doi.org/10.1214/23-ejp1039\">https://doi.org/10.1214/23-ejp1039</a>","ieee":"J. Jalowy, Z. Kabluchko, M. Löwe, and A. Marynych, “When does the chaos in the Curie-Weiss model stop to propagate?,” <i>Electronic Journal of Probability</i>, vol. 28, no. none, 2023, doi: <a href=\"https://doi.org/10.1214/23-ejp1039\">10.1214/23-ejp1039</a>.","chicago":"Jalowy, Jonas, Zakhar Kabluchko, Matthias Löwe, and Alexander Marynych. “When Does the Chaos in the Curie-Weiss Model Stop to Propagate?” <i>Electronic Journal of Probability</i> 28, no. none (2023). <a href=\"https://doi.org/10.1214/23-ejp1039\">https://doi.org/10.1214/23-ejp1039</a>.","ama":"Jalowy J, Kabluchko Z, Löwe M, Marynych A. When does the chaos in the Curie-Weiss model stop to propagate? <i>Electronic Journal of Probability</i>. 2023;28(none). doi:<a href=\"https://doi.org/10.1214/23-ejp1039\">10.1214/23-ejp1039</a>"},"intvolume":"        28","year":"2023","date_created":"2025-03-31T07:15:02Z","author":[{"id":"113768","full_name":"Jalowy, Jonas","last_name":"Jalowy","orcid":"0000-0001-9624-2685","first_name":"Jonas"},{"first_name":"Zakhar","full_name":"Kabluchko, Zakhar","last_name":"Kabluchko"},{"full_name":"Löwe, Matthias","last_name":"Löwe","first_name":"Matthias"},{"full_name":"Marynych, Alexander","last_name":"Marynych","first_name":"Alexander"}],"volume":28,"publisher":"Institute of Mathematical Statistics","date_updated":"2025-04-23T14:36:13Z","doi":"10.1214/23-ejp1039","title":"When does the chaos in the Curie-Weiss model stop to propagate?"},{"author":[{"full_name":"Hall, Brian C.","last_name":"Hall","first_name":"Brian C."},{"first_name":"Ching-Wei","full_name":"Ho, Ching-Wei","last_name":"Ho"},{"last_name":"Jalowy","orcid":"0000-0001-9624-2685","full_name":"Jalowy, Jonas","id":"113768","first_name":"Jonas"},{"full_name":"Kabluchko, Zakhar","last_name":"Kabluchko","first_name":"Zakhar"}],"date_created":"2025-03-31T07:15:40Z","date_updated":"2025-04-23T14:38:56Z","title":"Roots of polynomials under repeated differentiation and repeated  applications of fractional differential operators","citation":{"mla":"Hall, Brian C., et al. “Roots of Polynomials under Repeated Differentiation and Repeated  Applications of Fractional Differential Operators.” <i>ArXiv:2312.14883</i>, 2023.","short":"B.C. Hall, C.-W. Ho, J. Jalowy, Z. Kabluchko, ArXiv:2312.14883 (2023).","bibtex":"@article{Hall_Ho_Jalowy_Kabluchko_2023, title={Roots of polynomials under repeated differentiation and repeated  applications of fractional differential operators}, journal={arXiv:2312.14883}, author={Hall, Brian C. and Ho, Ching-Wei and Jalowy, Jonas and Kabluchko, Zakhar}, year={2023} }","apa":"Hall, B. C., Ho, C.-W., Jalowy, J., &#38; Kabluchko, Z. (2023). Roots of polynomials under repeated differentiation and repeated  applications of fractional differential operators. In <i>arXiv:2312.14883</i>.","ama":"Hall BC, Ho C-W, Jalowy J, Kabluchko Z. Roots of polynomials under repeated differentiation and repeated  applications of fractional differential operators. <i>arXiv:231214883</i>. Published online 2023.","chicago":"Hall, Brian C., Ching-Wei Ho, Jonas Jalowy, and Zakhar Kabluchko. “Roots of Polynomials under Repeated Differentiation and Repeated  Applications of Fractional Differential Operators.” <i>ArXiv:2312.14883</i>, 2023.","ieee":"B. C. Hall, C.-W. Ho, J. Jalowy, and Z. Kabluchko, “Roots of polynomials under repeated differentiation and repeated  applications of fractional differential operators,” <i>arXiv:2312.14883</i>. 2023."},"year":"2023","user_id":"113768","external_id":{"arxiv":["2312.14883"]},"_id":"59209","language":[{"iso":"eng"}],"publication":"arXiv:2312.14883","type":"preprint","status":"public","abstract":[{"lang":"eng","text":"We start with a random polynomial $P^{N}$ of degree $N$ with independent\r\ncoefficients and consider a new polynomial $P_{t}^{N}$ obtained by repeated\r\napplications of a fraction differential operator of the form $z^{a}%\r\n(d/dz)^{b},$ where $a$ and $b$ are real numbers. When $b>0,$ we compute the\r\nlimiting root distribution $\\mu_{t}$ of $P_{t}^{N}$ as $N\\rightarrow\\infty.$ We\r\nshow that $\\mu_{t}$ is the push-forward of the limiting root distribution of\r\n$P^{N}$ under a transport map $T_{t}$. The map $T_{t}$ is defined by flowing\r\nalong the characteristic curves of the PDE satisfied by the log potential of\r\n$\\mu_{t}.$ In the special case of repeated differentiation, our results may be\r\ninterpreted as saying that the roots evolve radially \\textit{with constant\r\nspeed} until they hit the origin, at which point, they cease to exist. For\r\ngeneral $a$ and $b,$ the transport map $T_{t}$ has a free probability\r\ninterpretation as multiplication of an $R$-diagonal operator by an $R$-diagonal\r\n\"transport operator.\" As an application, we obtain a push-forward\r\ncharacterization of the free self-convolution semigroup $\\oplus$ of radial\r\nmeasures on $\\mathbb{C}$.\r\n  We also consider the case $b<0,$ which includes the case of repeated\r\nintegration. More complicated behavior of the roots can occur in this case."}]},{"type":"preprint","publication":"arXiv:2308.11685","abstract":[{"text":"We investigate the evolution of the empirical distribution of the complex\r\nroots of high-degree random polynomials, when the polynomial undergoes the heat\r\nflow. In one prominent example of Weyl polynomials, the limiting zero\r\ndistribution evolves from the circular law into the elliptic law until it\r\ncollapses to the Wigner semicircle law, as was recently conjectured for\r\ncharacteristic polynomials of random matrices by Hall and Ho, 2022. Moreover,\r\nfor a general family of random polynomials with independent coefficients and\r\nisotropic limiting distribution of zeros, we determine the zero distribution of\r\nthe heat-evolved polynomials in terms of its logarithmic potential.\r\nFurthermore, we explicitly identify two critical time thresholds, at which\r\nsingularities develop and at which the limiting distribution collapses to the\r\nsemicircle law. We completely characterize the limiting root distribution of\r\nthe heat-evolved polynomials before singularities develop as the push-forward\r\nof the initial distribution under a transport map. Finally, we discuss the\r\nresults from the perspectives of partial differential equations (in particular\r\nHamilton-Jacobi equation and Burgers' equation), optimal transport, and free\r\nprobability. The theory is accompanied by explicit examples, simulations, and\r\nconjectures.","lang":"eng"}],"status":"public","external_id":{"arxiv":["2308.11685"]},"_id":"59187","user_id":"113768","language":[{"iso":"eng"}],"year":"2023","citation":{"ama":"Hall BC, Ho C-W, Jalowy J, Kabluchko Z. Zeros of random polynomials undergoing the heat flow. <i>arXiv:230811685</i>. Published online 2023.","chicago":"Hall, Brian C., Ching-Wei Ho, Jonas Jalowy, and Zakhar Kabluchko. “Zeros of Random Polynomials Undergoing the Heat Flow.” <i>ArXiv:2308.11685</i>, 2023.","ieee":"B. C. Hall, C.-W. Ho, J. Jalowy, and Z. Kabluchko, “Zeros of random polynomials undergoing the heat flow,” <i>arXiv:2308.11685</i>. 2023.","apa":"Hall, B. C., Ho, C.-W., Jalowy, J., &#38; Kabluchko, Z. (2023). Zeros of random polynomials undergoing the heat flow. In <i>arXiv:2308.11685</i>.","mla":"Hall, Brian C., et al. “Zeros of Random Polynomials Undergoing the Heat Flow.” <i>ArXiv:2308.11685</i>, 2023.","bibtex":"@article{Hall_Ho_Jalowy_Kabluchko_2023, title={Zeros of random polynomials undergoing the heat flow}, journal={arXiv:2308.11685}, author={Hall, Brian C. and Ho, Ching-Wei and Jalowy, Jonas and Kabluchko, Zakhar}, year={2023} }","short":"B.C. Hall, C.-W. Ho, J. Jalowy, Z. Kabluchko, ArXiv:2308.11685 (2023)."},"date_updated":"2025-04-23T14:38:41Z","author":[{"full_name":"Hall, Brian C.","last_name":"Hall","first_name":"Brian C."},{"first_name":"Ching-Wei","full_name":"Ho, Ching-Wei","last_name":"Ho"},{"first_name":"Jonas","full_name":"Jalowy, Jonas","id":"113768","orcid":"0000-0001-9624-2685","last_name":"Jalowy"},{"first_name":"Zakhar","last_name":"Kabluchko","full_name":"Kabluchko, Zakhar"}],"date_created":"2025-03-31T07:14:23Z","title":"Zeros of random polynomials undergoing the heat flow"},{"year":"2023","citation":{"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>ArXiv:2304.11145</i>, 2023.","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>arXiv:2304.11145</i>. 2023.","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>arXiv:230411145</i>. Published online 2023.","apa":"Erbar, M., Huesmann, M., Jalowy, J., &#38; Müller, B. (2023). Optimal transport of stationary point processes: Metric structure,  gradient flow and convexity of the specific entropy. In <i>arXiv:2304.11145</i>.","mla":"Erbar, Matthias, et al. “Optimal Transport of Stationary Point Processes: Metric Structure,  Gradient Flow and Convexity of the Specific Entropy.” <i>ArXiv:2304.11145</i>, 2023.","short":"M. Erbar, M. Huesmann, J. Jalowy, B. Müller, ArXiv:2304.11145 (2023).","bibtex":"@article{Erbar_Huesmann_Jalowy_Müller_2023, title={Optimal transport of stationary point processes: Metric structure,  gradient flow and convexity of the specific entropy}, journal={arXiv:2304.11145}, author={Erbar, Matthias and Huesmann, Martin and Jalowy, Jonas and Müller, Bastian}, year={2023} }"},"title":"Optimal transport of stationary point processes: Metric structure,  gradient flow and convexity of the specific entropy","date_updated":"2025-04-23T14:39:08Z","date_created":"2025-03-31T07:16:09Z","author":[{"last_name":"Erbar","full_name":"Erbar, Matthias","first_name":"Matthias"},{"first_name":"Martin","last_name":"Huesmann","full_name":"Huesmann, Martin"},{"id":"113768","full_name":"Jalowy, Jonas","last_name":"Jalowy","orcid":"0000-0001-9624-2685","first_name":"Jonas"},{"last_name":"Müller","full_name":"Müller, Bastian","first_name":"Bastian"}],"abstract":[{"lang":"eng","text":"We develop a theory of optimal transport for stationary random measures with\r\na focus on stationary point processes and construct a family of distances on\r\nthe set of stationary random measures. These induce a natural notion of\r\ninterpolation between two stationary random measures along a shortest curve\r\nconnecting them. In the setting of stationary point processes we leverage this\r\ntransport distance to give a geometric interpretation for the evolution of\r\ninfinite particle systems with stationary distribution. Namely, we characterise\r\nthe evolution of infinitely many Brownian motions as the gradient flow of the\r\nspecific relative entropy w.r.t.~the Poisson point process. Further, we\r\nestablish displacement convexity of the specific relative entropy along optimal\r\ninterpolations of point processes and establish an stationary analogue of the\r\nHWI inequality, relating specific entropy, transport distance, and a specific\r\nrelative Fisher information."}],"status":"public","publication":"arXiv:2304.11145","type":"preprint","language":[{"iso":"eng"}],"external_id":{"arxiv":["2304.11145"]},"_id":"59211","user_id":"113768"},{"citation":{"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>ArXiv:2304.11145</i>, 2023.","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>arXiv:2304.11145</i>. 2023.","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>arXiv:230411145</i>. Published online 2023.","apa":"Erbar, M., Huesmann, M., Jalowy, J., &#38; Müller, B. (2023). Optimal transport of stationary point processes: Metric structure,  gradient flow and convexity of the specific entropy. In <i>arXiv:2304.11145</i>.","short":"M. Erbar, M. Huesmann, J. Jalowy, B. Müller, ArXiv:2304.11145 (2023).","bibtex":"@article{Erbar_Huesmann_Jalowy_Müller_2023, title={Optimal transport of stationary point processes: Metric structure,  gradient flow and convexity of the specific entropy}, journal={arXiv:2304.11145}, author={Erbar, Matthias and Huesmann, Martin and Jalowy, Jonas and Müller, Bastian}, year={2023} }","mla":"Erbar, Matthias, et al. “Optimal Transport of Stationary Point Processes: Metric Structure,  Gradient Flow and Convexity of the Specific Entropy.” <i>ArXiv:2304.11145</i>, 2023."},"year":"2023","author":[{"first_name":"Matthias","last_name":"Erbar","full_name":"Erbar, Matthias"},{"last_name":"Huesmann","full_name":"Huesmann, Martin","first_name":"Martin"},{"first_name":"Jonas","orcid":"0000-0001-9624-2685","last_name":"Jalowy","full_name":"Jalowy, Jonas","id":"113768"},{"first_name":"Bastian","last_name":"Müller","full_name":"Müller, Bastian"}],"date_created":"2025-03-31T07:15:22Z","date_updated":"2025-04-23T14:38:52Z","title":"Optimal transport of stationary point processes: Metric structure,  gradient flow and convexity of the specific entropy","publication":"arXiv:2304.11145","type":"preprint","status":"public","abstract":[{"text":"We develop a theory of optimal transport for stationary random measures with\r\na focus on stationary point processes and construct a family of distances on\r\nthe set of stationary random measures. These induce a natural notion of\r\ninterpolation between two stationary random measures along a shortest curve\r\nconnecting them. In the setting of stationary point processes we leverage this\r\ntransport distance to give a geometric interpretation for the evolution of\r\ninfinite particle systems with stationary distribution. Namely, we characterise\r\nthe evolution of infinitely many Brownian motions as the gradient flow of the\r\nspecific relative entropy w.r.t.~the Poisson point process. Further, we\r\nestablish displacement convexity of the specific relative entropy along optimal\r\ninterpolations of point processes and establish an stationary analogue of the\r\nHWI inequality, relating specific entropy, transport distance, and a specific\r\nrelative Fisher information.","lang":"eng"}],"user_id":"113768","_id":"59189","external_id":{"arxiv":["2304.11145"]},"language":[{"iso":"eng"}]},{"publication_identifier":{"issn":["0246-0203"]},"publication_status":"published","issue":"4","year":"2023","intvolume":"        59","citation":{"chicago":"Jalowy, Jonas. “The Wasserstein Distance to the Circular Law.” <i>Annales de l’Institut Henri Poincaré, Probabilités et Statistiques</i> 59, no. 4 (2023). <a href=\"https://doi.org/10.1214/22-aihp1317\">https://doi.org/10.1214/22-aihp1317</a>.","ieee":"J. Jalowy, “The Wasserstein distance to the circular law,” <i>Annales de l’Institut Henri Poincaré, Probabilités et Statistiques</i>, vol. 59, no. 4, 2023, doi: <a href=\"https://doi.org/10.1214/22-aihp1317\">10.1214/22-aihp1317</a>.","ama":"Jalowy J. The Wasserstein distance to the circular law. <i>Annales de l’Institut Henri Poincaré, Probabilités et Statistiques</i>. 2023;59(4). doi:<a href=\"https://doi.org/10.1214/22-aihp1317\">10.1214/22-aihp1317</a>","apa":"Jalowy, J. (2023). The Wasserstein distance to the circular law. <i>Annales de l’Institut Henri Poincaré, Probabilités et Statistiques</i>, <i>59</i>(4). <a href=\"https://doi.org/10.1214/22-aihp1317\">https://doi.org/10.1214/22-aihp1317</a>","mla":"Jalowy, Jonas. “The Wasserstein Distance to the Circular Law.” <i>Annales de l’Institut Henri Poincaré, Probabilités et Statistiques</i>, vol. 59, no. 4, Institute of Mathematical Statistics, 2023, doi:<a href=\"https://doi.org/10.1214/22-aihp1317\">10.1214/22-aihp1317</a>.","bibtex":"@article{Jalowy_2023, title={The Wasserstein distance to the circular law}, volume={59}, DOI={<a href=\"https://doi.org/10.1214/22-aihp1317\">10.1214/22-aihp1317</a>}, number={4}, journal={Annales de l’Institut Henri Poincaré, Probabilités et Statistiques}, publisher={Institute of Mathematical Statistics}, author={Jalowy, Jonas}, year={2023} }","short":"J. Jalowy, Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 59 (2023)."},"date_updated":"2025-04-23T14:38:24Z","publisher":"Institute of Mathematical Statistics","volume":59,"date_created":"2025-03-31T07:12:40Z","author":[{"first_name":"Jonas","last_name":"Jalowy","orcid":"0000-0001-9624-2685","full_name":"Jalowy, Jonas","id":"113768"}],"title":"The Wasserstein distance to the circular law","doi":"10.1214/22-aihp1317","publication":"Annales de l'Institut Henri Poincaré, Probabilités et Statistiques","type":"journal_article","status":"public","_id":"59184","user_id":"113768","language":[{"iso":"eng"}]},{"year":"2023","citation":{"ama":"Hall B, Ho C-W, Jalowy J, Kabluchko Z. The heat flow, GAF, and SL(2;R). <i>arXiv:230406665</i>. Published online 2023.","ieee":"B. Hall, C.-W. Ho, J. Jalowy, and Z. Kabluchko, “The heat flow, GAF, and SL(2;R),” <i>arXiv:2304.06665</i>. 2023.","chicago":"Hall, Brian, Ching-Wei Ho, Jonas Jalowy, and Zakhar Kabluchko. “The Heat Flow, GAF, and SL(2;R).” <i>ArXiv:2304.06665</i>, 2023.","apa":"Hall, B., Ho, C.-W., Jalowy, J., &#38; Kabluchko, Z. (2023). The heat flow, GAF, and SL(2;R). In <i>arXiv:2304.06665</i>.","mla":"Hall, Brian, et al. “The Heat Flow, GAF, and SL(2;R).” <i>ArXiv:2304.06665</i>, 2023.","short":"B. Hall, C.-W. Ho, J. Jalowy, Z. Kabluchko, ArXiv:2304.06665 (2023).","bibtex":"@article{Hall_Ho_Jalowy_Kabluchko_2023, title={The heat flow, GAF, and SL(2;R)}, journal={arXiv:2304.06665}, author={Hall, Brian and Ho, Ching-Wei and Jalowy, Jonas and Kabluchko, Zakhar}, year={2023} }"},"title":"The heat flow, GAF, and SL(2;R)","date_updated":"2025-04-23T14:39:00Z","date_created":"2025-03-31T07:15:53Z","author":[{"first_name":"Brian","last_name":"Hall","full_name":"Hall, Brian"},{"first_name":"Ching-Wei","full_name":"Ho, Ching-Wei","last_name":"Ho"},{"orcid":"0000-0001-9624-2685","last_name":"Jalowy","full_name":"Jalowy, Jonas","id":"113768","first_name":"Jonas"},{"full_name":"Kabluchko, Zakhar","last_name":"Kabluchko","first_name":"Zakhar"}],"abstract":[{"text":"We establish basic properties of the heat flow on entire holomorphic\r\nfunctions that have order at most 2. We then look specifically at the action of\r\nthe heat flow on the Gaussian analytic function (GAF). We show that applying\r\nthe heat flow to a GAF and then rescaling and multiplying by an exponential of\r\na quadratic function gives another GAF. It follows that the zeros of the GAF\r\nare invariant in distribution under the heat flow, up to a simple rescaling.\r\n  We then show that the zeros of the GAF evolve under the heat flow\r\napproximately along straight lines, with an error whose distribution is\r\nindependent of the starting point. Finally, we connect the heat flow on the GAF\r\nto the metaplectic representation of the double cover of the group\r\n$SL(2;\\mathbb{R}).$","lang":"eng"}],"status":"public","type":"preprint","publication":"arXiv:2304.06665","language":[{"iso":"eng"}],"_id":"59210","external_id":{"arxiv":["2304.06665"]},"user_id":"113768"},{"publication":"Journal of Statistical Physics","type":"journal_article","abstract":[{"text":"<jats:title>Abstract</jats:title><jats:p>In this note we study the block spin mean-field Potts model, in which the spins are divided into <jats:italic>s</jats:italic> blocks and can take <jats:inline-formula><jats:alternatives><jats:tex-math>$$q\\ge 2$$</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                  <mml:mrow>\r\n                    <mml:mi>q</mml:mi>\r\n                    <mml:mo>≥</mml:mo>\r\n                    <mml:mn>2</mml:mn>\r\n                  </mml:mrow>\r\n                </mml:math></jats:alternatives></jats:inline-formula> different values (colors). Each block is allowed to contain a different proportion of vertices and behaves itself like a mean-field Ising/Potts model which also interacts with other blocks according to different temperatures. Of particular interest is the behavior of the magnetization, which counts the number of colors appearing in the distinct blocks. We prove central limit theorems for the magnetization in the generalized high-temperature regime and provide a moderate deviation principle for its fluctuations on lower scalings. More precisely, the magnetization concentrates around the uniform vector of all colors with an explicit, but singular, Gaussian distribution. In order to remove the singular component, we will also consider a rotated magnetization, which enables us to compare our results to various related models.</jats:p>","lang":"eng"}],"status":"public","_id":"59186","user_id":"113768","article_number":"3","language":[{"iso":"eng"}],"publication_identifier":{"issn":["0022-4715","1572-9613"]},"publication_status":"published","issue":"1","year":"2022","intvolume":"       187","citation":{"mla":"Jalowy, Jonas, et al. “Fluctuations of the Magnetization in the Block Potts Model.” <i>Journal of Statistical Physics</i>, vol. 187, no. 1, 3, Springer Science and Business Media LLC, 2022, doi:<a href=\"https://doi.org/10.1007/s10955-022-02889-4\">10.1007/s10955-022-02889-4</a>.","bibtex":"@article{Jalowy_Löwe_Sambale_2022, title={Fluctuations of the Magnetization in the Block Potts Model}, volume={187}, DOI={<a href=\"https://doi.org/10.1007/s10955-022-02889-4\">10.1007/s10955-022-02889-4</a>}, number={13}, journal={Journal of Statistical Physics}, publisher={Springer Science and Business Media LLC}, author={Jalowy, Jonas and Löwe, Matthias and Sambale, Holger}, year={2022} }","short":"J. Jalowy, M. Löwe, H. Sambale, Journal of Statistical Physics 187 (2022).","apa":"Jalowy, J., Löwe, M., &#38; Sambale, H. (2022). Fluctuations of the Magnetization in the Block Potts Model. <i>Journal of Statistical Physics</i>, <i>187</i>(1), Article 3. <a href=\"https://doi.org/10.1007/s10955-022-02889-4\">https://doi.org/10.1007/s10955-022-02889-4</a>","ieee":"J. Jalowy, M. Löwe, and H. Sambale, “Fluctuations of the Magnetization in the Block Potts Model,” <i>Journal of Statistical Physics</i>, vol. 187, no. 1, Art. no. 3, 2022, doi: <a href=\"https://doi.org/10.1007/s10955-022-02889-4\">10.1007/s10955-022-02889-4</a>.","chicago":"Jalowy, Jonas, Matthias Löwe, and Holger Sambale. “Fluctuations of the Magnetization in the Block Potts Model.” <i>Journal of Statistical Physics</i> 187, no. 1 (2022). <a href=\"https://doi.org/10.1007/s10955-022-02889-4\">https://doi.org/10.1007/s10955-022-02889-4</a>.","ama":"Jalowy J, Löwe M, Sambale H. Fluctuations of the Magnetization in the Block Potts Model. <i>Journal of Statistical Physics</i>. 2022;187(1). doi:<a href=\"https://doi.org/10.1007/s10955-022-02889-4\">10.1007/s10955-022-02889-4</a>"},"date_updated":"2025-04-23T14:38:45Z","publisher":"Springer Science and Business Media LLC","volume":187,"author":[{"first_name":"Jonas","last_name":"Jalowy","orcid":"0000-0001-9624-2685","id":"113768","full_name":"Jalowy, Jonas"},{"last_name":"Löwe","full_name":"Löwe, Matthias","first_name":"Matthias"},{"first_name":"Holger","last_name":"Sambale","full_name":"Sambale, Holger"}],"date_created":"2025-03-31T07:14:09Z","title":"Fluctuations of the Magnetization in the Block Potts Model","doi":"10.1007/s10955-022-02889-4"},{"year":"2021","citation":{"ama":"Jalowy J. Rate of convergence for products of independent non-Hermitian random matrices. <i>Electronic Journal of Probability</i>. 2021;26(none). doi:<a href=\"https://doi.org/10.1214/21-ejp625\">10.1214/21-ejp625</a>","chicago":"Jalowy, Jonas. “Rate of Convergence for Products of Independent Non-Hermitian Random Matrices.” <i>Electronic Journal of Probability</i> 26, no. none (2021). <a href=\"https://doi.org/10.1214/21-ejp625\">https://doi.org/10.1214/21-ejp625</a>.","ieee":"J. Jalowy, “Rate of convergence for products of independent non-Hermitian random matrices,” <i>Electronic Journal of Probability</i>, vol. 26, no. none, 2021, doi: <a href=\"https://doi.org/10.1214/21-ejp625\">10.1214/21-ejp625</a>.","short":"J. Jalowy, Electronic Journal of Probability 26 (2021).","mla":"Jalowy, Jonas. “Rate of Convergence for Products of Independent Non-Hermitian Random Matrices.” <i>Electronic Journal of Probability</i>, vol. 26, no. none, Institute of Mathematical Statistics, 2021, doi:<a href=\"https://doi.org/10.1214/21-ejp625\">10.1214/21-ejp625</a>.","bibtex":"@article{Jalowy_2021, title={Rate of convergence for products of independent non-Hermitian random matrices}, volume={26}, DOI={<a href=\"https://doi.org/10.1214/21-ejp625\">10.1214/21-ejp625</a>}, number={none}, journal={Electronic Journal of Probability}, publisher={Institute of Mathematical Statistics}, author={Jalowy, Jonas}, year={2021} }","apa":"Jalowy, J. (2021). Rate of convergence for products of independent non-Hermitian random matrices. <i>Electronic Journal of Probability</i>, <i>26</i>(none). <a href=\"https://doi.org/10.1214/21-ejp625\">https://doi.org/10.1214/21-ejp625</a>"},"intvolume":"        26","publication_status":"published","publication_identifier":{"issn":["1083-6489"]},"issue":"none","title":"Rate of convergence for products of independent non-Hermitian random matrices","doi":"10.1214/21-ejp625","date_updated":"2025-04-23T14:38:37Z","publisher":"Institute of Mathematical Statistics","date_created":"2025-03-31T07:13:44Z","author":[{"first_name":"Jonas","id":"113768","full_name":"Jalowy, Jonas","orcid":"0000-0001-9624-2685","last_name":"Jalowy"}],"volume":26,"status":"public","type":"journal_article","publication":"Electronic Journal of Probability","language":[{"iso":"eng"}],"_id":"59185","user_id":"113768"},{"language":[{"iso":"eng"}],"_id":"59214","user_id":"113768","status":"public","type":"journal_article","publication":"Electronic Communications in Probability","title":"Reconstructing a recurrent random environment from a single trajectory of a Random Walk in Random Environment with errors","doi":"10.1214/21-ecp425","publisher":"Institute of Mathematical Statistics","date_updated":"2025-04-23T14:39:18Z","author":[{"last_name":"Jalowy","orcid":"0000-0001-9624-2685","id":"113768","full_name":"Jalowy, Jonas","first_name":"Jonas"},{"first_name":"Matthias","full_name":"Löwe, Matthias","last_name":"Löwe"}],"date_created":"2025-03-31T07:17:34Z","volume":26,"year":"2021","citation":{"ama":"Jalowy J, Löwe M. Reconstructing a recurrent random environment from a single trajectory of a Random Walk in Random Environment with errors. <i>Electronic Communications in Probability</i>. 2021;26(none). doi:<a href=\"https://doi.org/10.1214/21-ecp425\">10.1214/21-ecp425</a>","chicago":"Jalowy, Jonas, and Matthias Löwe. “Reconstructing a Recurrent Random Environment from a Single Trajectory of a Random Walk in Random Environment with Errors.” <i>Electronic Communications in Probability</i> 26, no. none (2021). <a href=\"https://doi.org/10.1214/21-ecp425\">https://doi.org/10.1214/21-ecp425</a>.","ieee":"J. Jalowy and M. Löwe, “Reconstructing a recurrent random environment from a single trajectory of a Random Walk in Random Environment with errors,” <i>Electronic Communications in Probability</i>, vol. 26, no. none, 2021, doi: <a href=\"https://doi.org/10.1214/21-ecp425\">10.1214/21-ecp425</a>.","mla":"Jalowy, Jonas, and Matthias Löwe. “Reconstructing a Recurrent Random Environment from a Single Trajectory of a Random Walk in Random Environment with Errors.” <i>Electronic Communications in Probability</i>, vol. 26, no. none, Institute of Mathematical Statistics, 2021, doi:<a href=\"https://doi.org/10.1214/21-ecp425\">10.1214/21-ecp425</a>.","bibtex":"@article{Jalowy_Löwe_2021, title={Reconstructing a recurrent random environment from a single trajectory of a Random Walk in Random Environment with errors}, volume={26}, DOI={<a href=\"https://doi.org/10.1214/21-ecp425\">10.1214/21-ecp425</a>}, number={none}, journal={Electronic Communications in Probability}, publisher={Institute of Mathematical Statistics}, author={Jalowy, Jonas and Löwe, Matthias}, year={2021} }","short":"J. Jalowy, M. Löwe, Electronic Communications in Probability 26 (2021).","apa":"Jalowy, J., &#38; Löwe, M. (2021). Reconstructing a recurrent random environment from a single trajectory of a Random Walk in Random Environment with errors. <i>Electronic Communications in Probability</i>, <i>26</i>(none). <a href=\"https://doi.org/10.1214/21-ecp425\">https://doi.org/10.1214/21-ecp425</a>"},"intvolume":"        26","publication_status":"published","publication_identifier":{"issn":["1083-589X"]},"issue":"none"},{"citation":{"apa":"Götze, F., &#38; Jalowy, J. (2020). Rate of convergence to the Circular Law via smoothing inequalities for log-potentials. <i>Random Matrices: Theory and Applications</i>, <i>10</i>(03), Article 2150026. <a href=\"https://doi.org/10.1142/s201032632150026x\">https://doi.org/10.1142/s201032632150026x</a>","mla":"Götze, Friedrich, and Jonas Jalowy. “Rate of Convergence to the Circular Law via Smoothing Inequalities for Log-Potentials.” <i>Random Matrices: Theory and Applications</i>, vol. 10, no. 03, 2150026, World Scientific Pub Co Pte Lt, 2020, doi:<a href=\"https://doi.org/10.1142/s201032632150026x\">10.1142/s201032632150026x</a>.","bibtex":"@article{Götze_Jalowy_2020, title={Rate of convergence to the Circular Law via smoothing inequalities for log-potentials}, volume={10}, DOI={<a href=\"https://doi.org/10.1142/s201032632150026x\">10.1142/s201032632150026x</a>}, number={032150026}, journal={Random Matrices: Theory and Applications}, publisher={World Scientific Pub Co Pte Lt}, author={Götze, Friedrich and Jalowy, Jonas}, year={2020} }","short":"F. Götze, J. Jalowy, Random Matrices: Theory and Applications 10 (2020).","chicago":"Götze, Friedrich, and Jonas Jalowy. “Rate of Convergence to the Circular Law via Smoothing Inequalities for Log-Potentials.” <i>Random Matrices: Theory and Applications</i> 10, no. 03 (2020). <a href=\"https://doi.org/10.1142/s201032632150026x\">https://doi.org/10.1142/s201032632150026x</a>.","ieee":"F. Götze and J. Jalowy, “Rate of convergence to the Circular Law via smoothing inequalities for log-potentials,” <i>Random Matrices: Theory and Applications</i>, vol. 10, no. 03, Art. no. 2150026, 2020, doi: <a href=\"https://doi.org/10.1142/s201032632150026x\">10.1142/s201032632150026x</a>.","ama":"Götze F, Jalowy J. Rate of convergence to the Circular Law via smoothing inequalities for log-potentials. <i>Random Matrices: Theory and Applications</i>. 2020;10(03). doi:<a href=\"https://doi.org/10.1142/s201032632150026x\">10.1142/s201032632150026x</a>"},"intvolume":"        10","year":"2020","issue":"03","publication_status":"published","publication_identifier":{"issn":["2010-3263","2010-3271"]},"doi":"10.1142/s201032632150026x","title":"Rate of convergence to the Circular Law via smoothing inequalities for log-potentials","author":[{"first_name":"Friedrich","last_name":"Götze","full_name":"Götze, Friedrich"},{"full_name":"Jalowy, Jonas","id":"113768","last_name":"Jalowy","orcid":"0000-0001-9624-2685","first_name":"Jonas"}],"date_created":"2025-03-31T07:12:18Z","volume":10,"publisher":"World Scientific Pub Co Pte Lt","date_updated":"2025-04-23T14:38:18Z","status":"public","abstract":[{"lang":"eng","text":"<jats:p> The aim of this paper is to investigate the Kolmogorov distance of the Circular Law to the empirical spectral distribution of non-Hermitian random matrices with independent entries. The optimal rate of convergence is determined by the Ginibre ensemble and is given by [Formula: see text]. A smoothing inequality for complex measures that quantitatively relates the uniform Kolmogorov-like distance to the concentration of logarithmic potentials is shown. Combining it with results from Local Circular Laws, we apply it to prove nearly optimal rate of convergence to the Circular Law in Kolmogorov distance. Furthermore, we show that the same rate of convergence holds for the empirical measure of the roots of Weyl random polynomials. </jats:p>"}],"type":"journal_article","publication":"Random Matrices: Theory and Applications","language":[{"iso":"eng"}],"article_number":"2150026","user_id":"113768","_id":"59183"}]