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Multivariate Bessel processes describe the stochastic dynamics of interactingparticle systems of Calogero-Moser-Sutherland type and are related with$\beta$-Hermite and Laguerre ensembles. It was shown by Andraus, Katori, andMiyashita that for fixed starting points, these processes admit interestinglimit laws when the multiplicities $k$ tend to $\infty$, where in some casesthe limits are described by the zeros of classical Hermite and Laguerrepolynomials. In this paper we use SDEs to derive corresponding limit laws forstarting points of the form $\sqrt k\cdot x$ for $k\to\infty$ with $x$ in theinterior of the corresponding Weyl chambers. Our limit results are a.s. locallyuniform in time. Moreover, in some cases we present associated central limittheorems.

Limit theorems for multivariate Bessel processes in the freezing regime