Uniform approximation of eigenvalues in Laguerre and Hermite beta-ensembles by roots of orthogonal polynomials

We derive strong uniform approximations for the eigenvalues in general Laguerre and Hermite beta-ensembles by showing that the maximal discrepancy between the suitably scaled eigenvalues and roots of orthogonal polynomials converges almost surely to zero when the dimension converges to infinity. We also provide estimates of the rate of convergence.

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Year of publication:	2004
Authors:	Imhof, Lorens A. ; Dette, Holger
Publisher:	Dortmund : Universität Dortmund, Sonderforschungsbereich 475 - Komplexitätsreduktion in Multivariaten Datenstrukturen
Subject:	Gaussian ensemble \| random matrix \| rate of convergence \| Weyl?s inequality \| Wishart matrix

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Series:	Technical Report ; 2004,57
Type of publication:	Book / Working Paper
Type of publication (narrower categories):	Working Paper
Language:	English
Other identifiers:	479043159 [GVK] hdl:10419/22570 [Handle] RePEc:zbw:sfb475:200457 [RePEc]
Source:	EconStor

Persistent link: https://ebvufind01.dmz1.zbw.eu/10010296641