The beta-Hermite and beta-Laguerre processes

TL;DR

This paper introduces matrix-valued diffusion processes for beta-Hermite and beta-Laguerre ensembles, analyzing their spectral and empirical measures and their limit behaviors.

Contribution

It presents new matrix diffusion models for beta ensembles and studies their spectral measure processes and limit laws.

Findings

Defined matrix-valued diffusion processes for beta ensembles

Analyzed spectral measure and empirical processes

Established limit laws for these processes

Abstract

In this work, we introduce matrix-valued diffusion processes which describe the non-equilibrium situation of the matrix models for the beta-Hermite and the beta-Laguerre ensembles. We also study the corresponding spectral measure process and empirical/singular value process with regard to their limit laws.