Authors: | Voit, Michael Woerner, Jeannette H.C. |
Title: | Functional central limit theorems for multivariate Bessel processes in the freezing regime |
Language (ISO): | en |
Abstract: | Multivariate Bessel processes $(X_{t,k})_{t\ge0}$ 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 $(X_{t,k})_{t\ge0}$ 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. |
Subject Headings: | interacting particle systems Calogero-Moser-Sutherland models functional central limit theorems zeros of Hermite polynomials zeros of Laguerre polynomials Hermite ensembles Laguerre ensembles Dyson Brownian motion |
URI: | http://hdl.handle.net/2003/38160 http://dx.doi.org/10.17877/DE290R-20139 |
Issue Date: | 2019-01 |
Appears in Collections: | Preprints der Fakultät für Mathematik |
Files in This Item:
File | Description | Size | Format | |
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Preprint 2019-01.pdf | DNB | 462 kB | Adobe PDF | View/Open |
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