The differential equations associated with Calogero-Moser-Sutherland particle models in the freezing regime

Abstract

Multivariate Bessel processes describe Calogero-Moser-Sutherland particle models. They depend on a root system and a multiplicity $k$. Recently, several stochastic limit theorems for $k\to\infty$ were derived where the limits depend on the solutions of associated ODEs in these freezing regimes. In this paper we study these ODEs which are singular on the boundaries of their domains. We prove that for arbitrary initial conditions on the boundary, the ODEs have unique solutions in their domains for $t \gt 0$.