Beta Laguerre processes in a high temperature regime

Abstract

Beta Laguerre processes which are generalizations of the eigenvalue process of Wishart/Laguerre processes can be defined as the square of radial Dunkl processes of type B. In this paper, we study the limiting behavior of their empirical measure processes. By the moment method, we show the convergence to a limit in a high temperature regime, a regime where $\beta N \to const \in (0, \infty)$, where $\beta$ is the inverse temperature parameter and $N$ is the system size. This is a dynamic version of a recent result on the convergence of the empirical measures of beta Laguerre ensembles in the same regime.