Small Deviations for Beta Ensembles

Michel Ledoux (Université de Toulouse)
Brian Rider (University of Colorado Boulder)

Abstract


We establish various small deviation inequalities for the extremal (soft edge) eigenvalues in the beta-Hermite and beta-Laguerre ensembles. In both settings, upper bounds on the variance of the largest eigenvalue of the anticipated order follow immediately.

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Pages: 1319-1343

Publication Date: August 23, 2010

DOI: 10.1214/EJP.v15-798

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