Central limit theorems for multivariate Bessel processes in the freezing regime

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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 n...