Beta Laguerre processes in a high temperature regime

Hoang Dung Trinh and Khanh Duy Trinh

Stochastic Processes and their Applications, 2021, vol. 136, issue C, 192-205

Abstract: Beta Laguerre processes which are generalizations of the eigenvalue process of Wishart/Laguerre processes can be defined as the squares 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 βN→const∈(0,∞), where β 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.

Keywords: Beta Laguerre processes; Radial Dunkl processes; Beta Laguerre ensembles; High temperature regime; The moment method (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1016/j.spa.2021.03.002

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