Functional central limit theorems for multivariate Bessel processes in the freezing regime

Abstract

Multivariate Bessel processes $(X_{t,k}{)}_{t\ge 0}$ describe interacting particle systems of Calogero-Moser-Sutherland type and are related with $\beta$-Hermite and $\beta$-Laguerre ensembles. They depend on a root system and a multiplicity $k$ which corresponds to the parameter $\beta$ in random matrix theory. In the recent years, several limit theorems were derived for $k\to \infty$ with fixed $t>0$ and fixed starting point. Only recently, Andraus and Voit used the stochastic differential equations of $(X_{t,k}{)}_{t\ge 0}$ to derive limit theorems for $k\to \infty$ with starting points of the form $\sqrt{k}\cdot x$ with $x$ in the interior of the corresponding Weyl chambers. Here we provide associated functional central limit theorems which are locally uniform in $t$. The Gaussian limiting processes admit explicit representations in terms of matrix exponentials and the solutions of the associated deterministic dynamical systems.

arXiv commentThis is an abridged version of the previous paper without the ODE parts. The ODE part in an extended form can be found in Arxiv:1910.07888

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Cited by in corpus (3)

• Limit theorems and soft edge of freezing random matrix models via dual orthogonal polynomials
• Limit theorems for Jacobi ensembles with large parameters
• On the differential equations of frozen Calogero-Moser-Sutherland particle models