Functional central limit theorems for multivariate Bessel processes in the freezing regime
| dc.contributor.author | Voit, Michael | |
| dc.contributor.author | Woerner, Jeannette H.C. | |
| dc.date.accessioned | 2019-08-02T13:30:21Z | |
| dc.date.available | 2019-08-02T13:30:21Z | |
| dc.date.issued | 2019-01 | |
| dc.description.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. | en |
| dc.identifier.uri | http://hdl.handle.net/2003/38160 | |
| dc.identifier.uri | http://dx.doi.org/10.17877/DE290R-20139 | |
| dc.language.iso | en | |
| dc.subject | interacting particle systems | en |
| dc.subject | Calogero-Moser-Sutherland models | en |
| dc.subject | functional central limit theorems | en |
| dc.subject | zeros of Hermite polynomials | en |
| dc.subject | zeros of Laguerre polynomials | en |
| dc.subject | Hermite ensembles | en |
| dc.subject | Laguerre ensembles | en |
| dc.subject | Dyson Brownian motion | en |
| dc.subject.ddc | 610 | |
| dc.title | Functional central limit theorems for multivariate Bessel processes in the freezing regime | en |
| dc.type | Text | de |
| dc.type.publicationtype | preprint | en |
| dcterms.accessRights | open access | |
| eldorado.secondarypublication | false |