|Title:||Central limit theorems for multivariate Bessel processes in the freezing regime|
|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|
central limit theorems
Dyson Brownian motion
|Appears in Collections:||Preprints der Fakultät für Mathematik|
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