Authors: | Voit, Michael |
Title: | Central limit theorems for multivariate Bessel processes in the freezing regime |
Language (ISO): | en |
Abstract: | Multivariate Bessel processes (X_(t,k) )t≥0 are classified via associated root systems and multiplicity constants k ≥ 0. They describe the dynamics of interacting particle systems of Calogero-Moser-Sutherland type. Recently, Andraus, Katori, and Miyashita derived some weak laws of large numbers for X_(t,k) for fixed times t > 0 and k→∞. In this paper we derive associated central limit theorems for the root systems of types A, B and D in an elementary way. In most cases, the limits will be normal distributions, but in the B-case there are freezing limits where distributions associated with the root system A or one-sided normal distributions on half-spaces appear. Our results are connected to central limit theorems of Dumitriu and Edelman for β-Hermite and β-Laguerre ensembles. |
Subject Headings: | interacting particle systems Calogero-Moser-Sutherland models central limit theorems Hermite ensembles Laguerre ensembles Dyson Brownian motion |
URI: | http://hdl.handle.net/2003/37862 http://dx.doi.org/10.17877/DE290R-19849 |
Issue Date: | 2018-11 |
Appears in Collections: | Preprints der Fakultät für Mathematik |
Files in This Item:
File | Description | Size | Format | |
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Preprint 2018_06.pdf | DNB | 399.68 kB | Adobe PDF | View/Open |
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