Differential operators and spectral distributions of invariant ensembles from the classical orthogonal polynomials. {T}he continuous case
type: Item
instance of: scholarly article
title: Differential operators and spectral distributions of invariant ensembles from the classical orthogonal polynomials. {T}he continuous case
zbMATH Open document ID: 1073.60037
published in: Electronic Journal of Probability
publication date: 2005-03-08T00:00:00Z
full work available at URL: https://eudml.org/doc/125204
full work available at URL: paper7.abs.html
review text: Empirical spectral distributions of complex random matrices from the Gaussian, Laguerre, and Jacobi unitary ensembles are studied by means of methods, based on the research by \textit{U. Haagerup} and \textit{S. Thorbjørnsen} [Expo. Math. 21, No. 4, 293--337 (2003; Zbl 1041.15018)]. In the framework of abstract Markov operators [see \textit{D. Bakry}, in: Lectures on probability theory. Lect. Notes Math. 1581, 1--114 (1994; Zbl 0856.47026)], differential equations for Laplace transforms of eigenfunction measures are obtained, which allows one to get the recurrence relations for the moments of these measures. The latter ones are employed to describe sharp small deviation inequalities on the largest eigenvalues.
Mathematics Subject Classification ID: 60F99
Mathematics Subject Classification ID: 33C99
Mathematics Subject Classification ID: 60J25
Mathematics Subject Classification ID: 60J60
Mathematics Subject Classification ID: 82B31
Mathematics Subject Classification ID: 82B44
zbMATH DE Number: 2142132
zbMATH Keywords: complex random matrix
zbMATH Keywords: Gaussian, Laguerre, and Jacobi unitary ensembles
zbMATH Keywords: Markov diffusion operators
zbMATH Keywords: arcsine law
zbMATH Keywords: Trace-Widom asymptotics
author: Michel Ledoux
reviewed by: Yuri Kozitsky
MaRDI profile type: Publication
DOI: 10.1214/EJP.V9-191
description: scientific article; zbMATH DE number 2142132