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.

arXiv comment15 pages

References in corpus (8)

• Matrix Models for Beta Ensembles
• The Calogero-Sutherland Model and Generalized Classical Polynomials
• Symmetry of matrix-valued stochastic processes and noncolliding diffusion particle systems
• Global spectrum fluctuations for the $\beta$-Hermite and $\beta$-Laguerre ensembles via matrix models
• Invariant $\beta$-Wishart ensembles, crossover densities and asymptotic corrections to the Marchenko-Pastur law
• The Laguerre process and generalized Hartman--Watson law
• An exactly solvable self-convolutive recurrence
• Radial Dunkl Processes : Existence and uniqueness, Hitting time, Beta Processes and Random Matrices

Cited by in corpus (4)

• Beta Jacobi ensembles and associated Jacobi polynomials
• Limit theorems for moment processes of beta Dyson's Brownian motions and beta Laguerre processes
• Classical beta ensembles and related eigenvalues processes at high temperature and the Markov--Krein transform
• Functional Equations Solving Initial-Value Problems of Complex Burgers-Type Equations for One-Dimensional Log-Gases