Small Deviations for Beta Ensembles

Michel Ledoux; Brian Rider

doi:10.1214/EJP.v15-798

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Home > Journals > Electron. J. Probab. > Volume 15 > Article

2010 Small Deviations for Beta Ensembles

Michel Ledoux, Brian Rider

Author Affiliations +

Michel Ledoux,¹ Brian Rider²
¹Université de Toulouse
²University of Colorado Boulder

Electron. J. Probab. 15: 1319-1343 (2010). DOI: 10.1214/EJP.v15-798

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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.