@unpublished{64816,
  abstract     = {{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 $s_N=N$.
  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 $s_N \to \infty$.}},
  author       = {{Jalowy, Jonas and Lammers, Isabel and Löwe, Matthias}},
  booktitle    = {{arXiv:2603.01994}},
  title        = {{{The infinite block spin Ising model}}},
  year         = {{2026}},
}

@article{65745,
  abstract     = {{<jats:title>Abstract</jats:title>
                  <jats:p>In this work, we address the numerical identification of entanglement in dynamical scenarios. To this end, we consider different programs based on the restriction of the evolution to the set of separable (i.e., non-entangled) states, together with the discretization of the space of variables for numerical computations. As a first approach, we apply linear splitting methods to the restricted, continuous equations of motion derived from variational principles. We utilize an exchange interaction Hamiltonian to confirm that the numerical and analytical solutions coincide in the limit of small time steps. The application to different Hamiltonians shows the wide applicability of the method to detect dynamical entanglement. To avoid the derivation of analytical solutions for complex dynamics, we consider variational, numerical integration schemes, introducing a variational discretization for Lagrangians linear in velocities. Here, we examine and compare two approaches: one in which the system is discretized before the restriction is applied, and another in which the restriction precedes the discretization. We find that the "first-discretize-then-restrict" method becomes numerically unstable, already for the example of an exchange-interaction Hamiltonian, which can be an important consideration for the numerical analysis of constrained quantum dynamics. Thereby, broadly applicable numerical tools, including their limitations, for studying entanglement over time are established for assessing the entangling power of processes that are used in quantum information theory.</jats:p>}},
  author       = {{Offen, Christian and Wembe, Boris and Ares, Laura and Sperling, Jan and Ober-Blöbaum, Sina}},
  issn         = {{1751-8113}},
  journal      = {{Journal of Physics A: Mathematical and Theoretical}},
  publisher    = {{IOP Publishing}},
  title        = {{{Numerical approaches to entangling dynamics from variational principles}}},
  doi          = {{10.1088/1751-8121/ae6d51}},
  year         = {{2026}},
}

@article{65742,
  abstract     = {{<jats:title>Abstract</jats:title>
                  <jats:p>In this work, we address the numerical identification of entanglement in dynamical scenarios. To this end, we consider different programs based on the restriction of the evolution to the set of separable (i.e., non-entangled) states, together with the discretization of the space of variables for numerical computations. As a first approach, we apply linear splitting methods to the restricted, continuous equations of motion derived from variational principles. We utilize an exchange interaction Hamiltonian to confirm that the numerical and analytical solutions coincide in the limit of small time steps. The application to different Hamiltonians shows the wide applicability of the method to detect dynamical entanglement. To avoid the derivation of analytical solutions for complex dynamics, we consider variational, numerical integration schemes, introducing a variational discretization for Lagrangians linear in velocities. Here, we examine and compare two approaches: one in which the system is discretized before the restriction is applied, and another in which the restriction precedes the discretization. We find that the "first-discretize-then-restrict" method becomes numerically unstable, already for the example of an exchange-interaction Hamiltonian, which can be an important consideration for the numerical analysis of constrained quantum dynamics. Thereby, broadly applicable numerical tools, including their limitations, for studying entanglement over time are established for assessing the entangling power of processes that are used in quantum information theory.</jats:p>}},
  author       = {{Offen, Christian and Wembe, Boris and Ares, Laura and Sperling, Jan and Ober-Blöbaum, Sina}},
  issn         = {{1751-8113}},
  journal      = {{Journal of Physics A: Mathematical and Theoretical}},
  publisher    = {{IOP Publishing}},
  title        = {{{Numerical approaches to entangling dynamics from variational principles}}},
  doi          = {{10.1088/1751-8121/ae6d51}},
  year         = {{2026}},
}

@inproceedings{65746,
  abstract     = {{This paper presents a class of structure-preserving numerical methods for quantum optimal control problems, based on commutator-free Cayley integrators. Starting from the Krotov framework, we reformulate the forward and backward propagation steps using Cayley-type schemes that preserve unitarity and symmetry at the discrete level. This approach eliminates the need for matrix exponentials and commutators, leading to significant computational savings while maintaining higher-order accuracy. We first recall the standard linear setting and then extend the formulation to nonlinear Schrödinger and Gross-Pitaevskii equations using a Cayley-polynomial interpolation strategy. Numerical experiments on state-transfer problems illustrate that the CF-Cayley method achieves the same accuracy as high-order exponential or Cayley-Magnus schemes at substantially lower cost, especially for longtime or highly oscillatory dynamics. In the nonlinear regime, the structure-preserving properties of the method ensure stability and norm conservation, making it a robust tool for large-scale quantum control simulations. The proposed framework thus bridges geometric integration and optimal control, offering an efficient and reliable alternative to existing exponential-based propagators.}},
  author       = {{Wembe Moafo, Boris Edgar and Ali, Usman and Meier, Torsten and Ober-Blöbaum, Sina}},
  location     = {{Reykjavík, Iceland}},
  title        = {{{Cayley Commutator-free Methods for Krotov-Type Algorithms in Quantum Optimal Control}}},
  doi          = {{10.48550/ARXIV.2603.11697}},
  year         = {{2026}},
}

@unpublished{65744,
  abstract     = {{Optimal control problems with symmetries often admit a non stationary turnpike property called trim turnpike, which characterizes the convergence of optimal solutions to certain symmetry induced trajectories called trim primitives. In this paper we establish an exponential trim turnpike property for a class of optimal control problems with structural properties related to Abelian Lie group symmetries. The key ingredient of our approach is the introduction of an appropriate reduced optimal control problem. We show that extremals of the original problem can be characterized through a reduced Hamiltonian boundary value problem that coincides with the optimality system of the reduced problem. Under a hyperbolicity assumption on the equilibrium of the corresponding reduced Hamiltonian system we prove that optimal trajectories remain exponentially close, up to boundary layers near the endpoints, to a trim primitive defined by the static reduced problem. The theoretical results are illustrated on three representative examples: linear and nonlinear problems with quadratic cost and the Kepler orbital transfer problem.}},
  author       = {{Maslovskaya, Sofya and Ober-Blöbaum, Sina and Wembe Moafo, Boris Edgar}},
  title        = {{{Non static exponential turnpike property for optimal control problems with symmetries and boundary conditions}}},
  year         = {{2026}},
}

@article{65747,
  abstract     = {{In this work, we address the numerical identification of entanglement in dynamical scenarios. To this end, we consider different programs based on the restriction of the evolution to the set of separable (i.e., non-entangled) states, together with the discretization of the space of variables for numerical computations. As a first approach, we apply linear splitting methods to the restricted, continuous equations of motion derived from variational principles. We utilize an exchange interaction Hamiltonian to confirm that the numerical and analytical solutions coincide in the limit of small time steps. The application to different Hamiltonians shows the wide applicability of the method to detect dynamical entanglement. To avoid the derivation of analytical solutions for complex dynamics, we consider variational, numerical integration schemes, introducing a variational discretization for Lagrangians linear in velocities. Here, we examine and compare two approaches: one in which the system is discretized before the restriction is applied, and another in which the restriction precedes the discretization. We find that the "first-discretize-then-restrict" method becomes numerically unstable, already for the example of an exchange-interaction Hamiltonian, which can be an important consideration for the numerical analysis of constrained quantum dynamics. Thereby, broadly applicable numerical tools, including their limitations, for studying entanglement over time are established for assessing the entangling power of processes that are used in quantum information theory.}},
  author       = {{Offen, Christian and Wembe, Boris and Ares, Laura and Sperling, Jan and Ober-Blöbaum, Sina}},
  issn         = {{1751-8113}},
  journal      = {{Journal of Physics A: Mathematical and Theoretical}},
  publisher    = {{IOP Publishing}},
  title        = {{{Numerical approaches to entangling dynamics from variational principles}}},
  doi          = {{10.1088/1751-8121/ae6d51}},
  year         = {{2026}},
}

@unpublished{66642,
  abstract     = {{In this work, we build a bridge between the Pólya--Schur program and Voiculescu's free probability theory. A cornerstone of the former is the Pólya--Benz Theorem, classifying a central family of real-root preserving operators on the space of polynomials, as those given by $f(\partial_z)$ for a Laguerre--Pólya function $f$ and the derivative operator $\partial_{z}$. We prove that any free (additive) infinitely divisible distribution can be attained as the weak limit of root distributions of Appell polynomials $f_n(\partial_z)z^n$ as $n\to\infty$, for a suitably chosen sequence $f_n$ of Laguerre--Pólya functions.
  Such questions on the (global) limiting distributions of real rooted polynomials belong to the active research area of finite free probability. In contrast to its standard tools, our approach allows for non-compactly supported limiting distributions, (barely) complex rooted polynomials and even provides the full microscopic description of the roots. Moreover, we extend our results to differential operators generating free multiplicative infinitely divisible distributions, to the rectangular free convolution, and to $f_n(\partial_z)p_n$ for real rooted polynomials $p_n$, implying a generalization of the recent connections between the heat flow and free Brownian motion to any free Lévy process.
  As corollaries, we identify free stable distributions by choosing $f_n$ to be a fixed rescaled Laguerre--Pólya function, and we prove various convergence results on the zero distributions of Jensen polynomials, e.g. the limiting root distribution of Jensen polynomial of the Riemann $Ξ$-function is given by the Cauchy distribution.}},
  author       = {{Campbell, Andrew and Jalowy, Jonas}},
  booktitle    = {{arXiv:2605.31356}},
  title        = {{{Pólya--Schur problems and free probability}}},
  year         = {{2026}},
}

@article{66641,
  author       = {{Jalowy, Jonas and Stange, Hanna}},
  issn         = {{0304-4149}},
  journal      = {{Stochastic Processes and their Applications}},
  publisher    = {{Elsevier BV}},
  title        = {{{Box-covariances of hyperuniform point processes}}},
  doi          = {{10.1016/j.spa.2026.104996}},
  volume       = {{199}},
  year         = {{2026}},
}

@unpublished{59664,
  abstract     = {{Given a sequence of polynomials $(P_n)_{n \in \mathbb{N}}$ with only
nonpositive zeros, the aim of this article is to present a user-friendly
approach for determining the limiting zero distribution of $P_n$ as
$\mathrm{deg}\, P_n \to \infty$. The method is based on establishing an
equivalence between the existence of a limiting empirical zero distribution
$\mu$ and the existence of an exponential profile $g$ associated with the
coefficients of the polynomials $(P_n)_{n \in \mathbb{N}}$. The exponential
profile $g$, which can be roughly described by $[z^k]P_n(z) \approx \exp(n
g(k/n))$, offers a direct route to computing the Cauchy transform $G$ of $\mu$:
the functions $t \mapsto tG(t)$ and $\alpha \mapsto \exp(-g'(\alpha))$ are
mutual inverses. This relationship, in various forms, has previously appeared
in the literature, most notably in the paper [Van Assche, Fano and Ortolani,
SIAM J. Math. Anal., 1987].
  As a first contribution, we present a self-contained probabilistic proof of
this equivalence by representing the polynomials as generating functions of
sums of independent Bernoulli random variables. This probabilistic framework
naturally lends itself to tools from large deviation theory, such as the
exponential change of measure. The resulting theorems generalize and unify a
range of previously known results, which were traditionally established through
analytic or combinatorial methods.
  Secondly, using the profile-based approach, we investigate how the
exponential profile and the limiting zero distribution behave under certain
operations on polynomials, including finite free convolutions, Hadamard
products, and repeated differentiation. In particular, our approach yields new
proofs of the convergence results `$\boxplus_n \to \boxplus$' and `$\boxtimes_n
\to \boxtimes$', extending them to cases where the distributions are not
necessarily compactly supported.}},
  author       = {{Jalowy, Jonas and Kabluchko, Zakhar and Marynych, Alexander}},
  booktitle    = {{arXiv:2504.11593}},
  title        = {{{Zeros and exponential profiles of polynomials I: Limit distributions,  finite free convolutions and repeated differentiation}}},
  year         = {{2025}},
}

@article{59665,
  author       = {{Erbar, Matthias and Huesmann, Martin and Jalowy, Jonas and Müller, Bastian}},
  issn         = {{0022-1236}},
  journal      = {{Journal of Functional Analysis}},
  number       = {{4}},
  publisher    = {{Elsevier BV}},
  title        = {{{Optimal transport of stationary point processes: Metric structure, gradient flow and convexity of the specific entropy}}},
  doi          = {{10.1016/j.jfa.2025.110974}},
  volume       = {{289}},
  year         = {{2025}},
}

@article{59507,
  abstract     = {{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.}},
  author       = {{Wembe Moafo, Boris Edgar and Offen, Cristian  and Maslovskaya, Sofya and Ober-Blöbaum, Sina and Singh, Pranav}},
  journal      = {{J. Comput. Appl. Math}},
  number       = {{15}},
  title        = {{{Commutator-free Cayley methods}}},
  doi          = {{10.1016/j.cam.2025.117184}},
  volume       = {{477}},
  year         = {{2025}},
}

@unpublished{63394,
  abstract     = {{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.}},
  author       = {{Byun, Sung-Soo and Jalowy, Jonas and Lee, Yong-Woo and Schehr, Grégory}},
  booktitle    = {{arXiv:2511.09191}},
  title        = {{{Moderate-to-large deviation asymptotics for real eigenvalues of the elliptic Ginibre matrices}}},
  year         = {{2025}},
}

@unpublished{63393,
  abstract     = {{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.}},
  author       = {{Höfert, Antonia and Jalowy, Jonas and Kabluchko, Zakhar}},
  booktitle    = {{arXiv:2512.17808}},
  title        = {{{Zeros of polynomial powers under the heat flow}}},
  year         = {{2025}},
}

@unpublished{60293,
  abstract     = {{In this work, we present a complete characterization of the covariance
structure of number statistics in boxes for hyperuniform point processes. Under
a standard integrability assumption, the covariance depends solely on the
overlap of the faces of the box. Beyond this assumption, a novel interpolating
covariance structure emerges. This enables us to identify a limiting Gaussian
'coarse-grained' process, counting the number of points in large boxes as a
function of the box position. Depending on the integrability assumption, this
process may be continuous or discontinuous, e.g. in d=1 it is given by an
increment process of a fractional Brownian motion.}},
  author       = {{Jalowy, Jonas and Stange, Hanna}},
  booktitle    = {{arXiv:2506.13661}},
  title        = {{{Box-Covariances of Hyperuniform Point Processes}}},
  year         = {{2025}},
}

@article{62291,
  abstract     = {{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.
 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.}},
  title        = {{{Zeros and exponential profiles of polynomials II: Examples}}},
  doi          = {{10.48550/ARXIV.2509.11248}},
  year         = {{2025}},
}

@article{53146,
  author       = {{Berger, Thomas and Dennstädt, Dario and Lanza, L.  and Worthmann, K. }},
  journal      = {{SIAM Journal on Control and Optimization}},
  title        = {{{Robust Funnel Model Predictive Control for Output Tracking with Prescribed Performance}}},
  year         = {{2024}},
}

@article{53142,
  author       = {{Berger, Thomas and Lanza, Lukas}},
  journal      = {{IMA Journal of Mathematical Control and Information,}},
  number       = {{4}},
  pages        = {{691--713}},
  title        = {{{Funnel control of linear systems with arbitrary relative degree under output measurement losses}}},
  doi          = {{doi: 10.1093/imamci/dnad029}},
  volume       = {{40}},
  year         = {{2023}},
}

@article{53143,
  author       = {{Lee, J. G. and Berger, Thomas and Trenn, S. and Shim, H.}},
  journal      = {{Automatica}},
  pages        = {{Article 111204}},
  title        = {{{Edge-wise funnel output synchronization of heterogeneous agents with relative degree one}}},
  doi          = {{doi: 10.1016/j.automatica.2023.111204 (open access)}},
  volume       = {{156}},
  year         = {{2023}},
}

@article{35644,
  author       = {{Kolb, Martin and Klump, Alexander}},
  journal      = {{Theory of Probability and its Applications}},
  number       = {{4}},
  pages        = {{717--744}},
  publisher    = {{Society for Industrial and Applied Mathematics}},
  title        = {{{Uniqueness of the Inverse First Passage Time Problem and the Shape of the Shiryaev boundary}}},
  volume       = {{67}},
  year         = {{2022}},
}

@article{35649,
  abstract     = {{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.}},
  author       = {{Kolb, Martin and Liesenfeld, Matthias}},
  journal      = {{Electronic Journal of Probability}},
  number       = {{27}},
  pages        = {{1--28}},
  publisher    = {{Institute of Mathematical Statistics}},
  title        = {{{On non-extinction in a Fleming-Viot-type particle model with Bessel drift}}},
  doi          = {{https://doi.org/10.1214/22-EJP866}},
  year         = {{2022}},
}