Voit, Michael2019-01-082019-01-082018-11http://hdl.handle.net/2003/3786210.17877/DE290R-19849Multivariate 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.eninteracting particle systemsCalogero-Moser-Sutherland modelscentral limit theoremsHermite ensemblesLaguerre ensemblesDyson Brownian motion610preprint