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dc.contributor.authorVoit, Michael-
dc.contributor.authorWoerner, Jeannette H.C.-
dc.date.accessioned2019-08-02T13:30:21Z-
dc.date.available2019-08-02T13:30:21Z-
dc.date.issued2019-01-
dc.identifier.urihttp://hdl.handle.net/2003/38160-
dc.identifier.urihttp://dx.doi.org/10.17877/DE290R-20139-
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.language.isoen-
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.subject.ddc610-
dc.titleFunctional central limit theorems for multivariate Bessel processes in the freezing regimeen
dc.typeTextde
dc.type.publicationtypepreprinten
dcterms.accessRightsopen access-
eldorado.secondarypublicationfalse-
Appears in Collections:Preprints der Fakultät für Mathematik

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