11 citations · 29 across the 18 of their papers we have counts for
19 papers
Heat flow and repeated differentiation of polynomials with i.i.d. roots
Jonas Jalowy
How do the zeros of a polynomial evolve under the holomorphic heat flow or repeated differentiation? In this work, we develop a unified probabilistic proof to three conjectures on…
Pólya--Schur problems and free probability
Andrew Campbell, Jonas Jalowy
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 cen…
The infinite block spin Ising model
Jonas Jalowy, Isabel Lammers, Matthias Löwe
We study a block mean-field Ising model with spins split into blocks, with Curie-Weiss interaction within blocks and nearest-neighbor coupling between blocks. While previ…
Zeros of polynomial powers under the heat flow
Antonia Höfert, Jonas Jalowy, Zakhar Kabluchko
We study the zero evolution of high powers of polynomials under the heat flow. For any fixed polynomial , we prove that the empirical zero distribution of its heat-evolved $n…
Moderate-to-large deviation asymptotics for real eigenvalues of the elliptic Ginibre matrices
Sung-Soo Byun, Jonas Jalowy, Yong-Woo Lee +1
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…
Zeros and exponential profiles of polynomials II: Examples
Jonas Jalowy, Zakhar Kabluchko, Alexander Marynych
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…
Box-Covariances of Hyperuniform Point Processes
Jonas Jalowy, Hanna Stange
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 assu…
Zeros and exponential profiles of polynomials I: Limit distributions, finite free convolutions and repeated differentiation
Jonas Jalowy, Zakhar Kabluchko, Alexander Marynych
Given a sequence of polynomials with only nonpositive zeros, the aim of this article is to present a user-friendly approach for determining the limiting…
Propagation of chaos and residual dependence in Gibbs measures on finite sets
Jonas Jalowy, Zakhar Kabluchko, Matthias Löwe
We compare a mean-field Gibbs distribution on a finite state space on spins to that of an explicit simple mixture of product measures. This illustrates the situation beyond the…
Roots of polynomials under repeated differentiation and repeated applications of fractional differential operators
Brian C. Hall, Ching-Wei Ho, Jonas Jalowy +1
We start with a random polynomial of degree with independent coefficients. We then consider a new polynomial obtained by applications o…
Zeros of random polynomials undergoing the heat flow
Brian C. Hall, Ching-Wei Ho, Jonas Jalowy +1
We investigate the evolution of the empirical distribution of the complex roots of high-degree random polynomials, when the polynomial undergoes the heat flow. In one prominent exa…
When does the chaos in the Curie-Weiss model stop to propagate?
Jonas Jalowy, Zakhar Kabluchko, Matthias Löwe +1
We investigate increasing propagation of chaos for the mean-field Ising model of ferromagnetism (also known as the Curie-Weiss model) with spins at inverse temperature an…
Optimal transport of stationary point processes: Metric structure, gradient flow and convexity of the specific entropy
Matthias Erbar, Martin Huesmann, Jonas Jalowy +1
We develop a theory of optimal transport for stationary random measures with a focus on stationary point processes and construct a family of distances on the set of stationary rand…
The heat flow, GAF, and SL(2;R)
Brian Hall, Ching-Wei Ho, Jonas Jalowy +1
We establish basic properties of the heat flow on entire holomorphic functions that have order at most 2. We then look specifically at the action of the heat flow on the Gaussian a…
The Wasserstein distance to the Circular Law
Jonas Jalowy
We investigate the Wasserstein distance between the empirical spectral distribution of non-Hermitian random matrices and the Circular Law. For general entry distributions, we obtai…
Fluctuations of the magnetization in the Block Potts Model
Jonas Jalowy, Matthias Löwe, Holger Sambale
In this note we study the block spin mean-field Potts model, in which the spins are divided into blocks and can take different values (colors). Each block is allowed t…
Reconstructing a (recurrent) random environment from a single trajectory of Random Walk in Random Environment with errors
Jonas Jalowy, Matthias Löwe
We consider one infinite path of a Random Walk in Random Environment (RWRE, for short) in an unknown environment. This environment consists of either i.i.d.\ site or bond randomnes…
Rate of convergence for products of independent non-Hermitian random matrices
Jonas Jalowy
We study the rate of convergence of the empirical spectral distribution of products of independent non-Hermitian random matrices to the power of the Circular Law. The distance to t…
Rate of Convergence to the Circular Law via Smoothing Inequalities for Log-Potentials
Friedrich Götze, Jonas Jalowy
The aim of this note is to investigate the Kolmogorov distance of the Circular Law to the empirical spectral distribution of non-Hermitian random matrices with independent entries.…