  Multivariate Bessel and Jacobi processes describe Calogero-Moser-Sutherland
particle models. They depend on a parameter $k$ and are related to
time-dependent classical random matrix models like Dysom Brownian motions,
where $k$ has the interpretation of an inverse temperature. There are several
stochastic limit theorems for $k\to\infty$ were the limits depend on the
solutions of associated ODEs where these ODEs admit particular simple solutions
which are connected with the zeros of the classical orthogonal polynomials. In
this paper we show that these solutions attract all solutions. Moreover we
present a connection between the solutions of these ODEs with associated
inverse heat equations. These inverse heat equations are used to compute the
expectations of some determinantal formulas for the Bessel and Jacobi
processes.
