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Differential Operators and Spectral Distributions of Invariant Ensembles from the Classical Orthogonal Polynomials. The Continuous Case

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1.	Title	Title of document	Differential Operators and Spectral Distributions of Invariant Ensembles from the Classical Orthogonal Polynomials. The Continuous Case
2.	Creator	Author's name, affiliation, country	Michel Ledoux; Université de Toulouse
3.	Subject	Discipline(s)
3.	Subject	Keyword(s)
4.	Description	Abstract	Following the investigation by U. Haagerup and S. Thorbjornsen, we present a simple differential approach to the limit theorems for empirical spectral distributions of complex random matrices from the Gaussian, Laguerre and Jacobi Unitary Ensembles. In the framework of abstract Markov diffusion operators, we derive by the integration by parts formula differential equations for Laplace transforms and recurrence equations for moments of eigenfunction measures. In particular, a new description of the equilibrium measures as adapted mixtures of the universal arcsine law with an independent uniform distribution is emphasized. The moment recurrence relations are used to describe sharp, non asymptotic, small deviation inequalities on the largest eigenvalues at the rate given by the Tracy-Widom asymptotics.
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)
7.	Date	(YYYY-MM-DD)	2004-02-25
8.	Type	Status & genre	Peer-reviewed Article
8.	Type	Type
9.	Format	File format	PDF
10.	Identifier	Uniform Resource Identifier	http://ejp.ejpecp.org/article/view/191
10.	Identifier	Digital Object Identifier	10.1214/EJP.v9-191
11.	Source	Journal/conference title; vol., no. (year)	Electronic Journal of Probability; Vol 9
12.	Language	English=en
14.	Coverage	Geo-spatial location, chronological period, research sample (gender, age, etc.)
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