Affiliation:
1. Department of Mathematics, The Royal Institute of Technology, 100 44 Stockholm, Sweden
Abstract
In this paper, we study tridiagonal random matrix models related to the classical β-ensembles (Gaussian, Laguerre, and Jacobi) in the high-temperature regime, i.e., when the size N of the matrix tends to infinity with the constraint that βN = 2 α constant, α > 0. We call these ensembles the Gaussian, Laguerre, and Jacobi α-ensembles, and we prove the convergence of their empirical spectral distributions to their mean densities of states, and we compute them explicitly. As an application, we explicitly compute the mean density of states of the Lax matrix of the Toda lattice with periodic boundary conditions with respect to the Gibbs ensemble.
Funder
HORIZON EUROPE Marie Sklodowska-Curie Actions
Gruppo Nazionale per la Fisica Matematica
Centre National de la Recherche Scientifique
Subject
Mathematical Physics,Statistical and Nonlinear Physics
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