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dc.contributor.authorVoit, Michael-
dc.contributor.authorWoerner, Jeannette H.C.-
dc.description.abstractMultivariate 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.en
dc.subjectinteracting particle systemsen
dc.subjectCalogero-Moser-Sutherland modelsen
dc.subjectfunctional central limit theoremsen
dc.subjectzeros of Hermite polynomialsen
dc.subjectzeros of Laguerre polynomialsen
dc.subjectHermite ensemblesen
dc.subjectLaguerre ensemblesen
dc.subjectDyson Brownian motionen
dc.titleFunctional central limit theorems for multivariate Bessel processes in the freezing regimeen
dcterms.accessRightsopen access-
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