Authors: Andraus, Sergio
Voit, Michael
Title: Limit theorems for multivariate Bessel processes in the freezing regime
Language (ISO): en
Abstract: Multivariate Bessel processes describe the stochastic dynamics of interacting particle systems of Calogero-Moser-Sutherland type and are related with β-Hermite and Laguerre ensembles. It was shown by Andraus, Katori, and Miyashita that for fixed starting points, these processes admit interesting limit laws when the multiplicities k tend to ∞, where in some cases the limits are described by the zeros of classical Hermite and Laguerre polynomials. In this paper we use SDEs to derive corresponding limit laws for starting points of the form √k∙x for k→∞ with x in the interior of the corresponding Weyl chambers. Our limit results are a.s. locally uniform in time. Moreover, in some cases we present associated central limit theorems.
Subject Headings: interacting particle systems
Calogero-Moser-Sutherland models
strong limiting laws
central limit theorems
zeros of Hermite polynomials
zeros of Laguerre polynomials
Hermite ensembles
Laguerre ensembles
Issue Date: 2018-11
Appears in Collections:Preprints der Fakultät für Mathematik

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