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2016 Near-extreme eigenvalues in the beta-ensembles
Catherine Donati-Martin, Alain Rouault
Electron. J. Probab. 21: 1-17 (2016). DOI: 10.1214/16-EJP4

Abstract

For beta-ensembles with convex polynomial potentials, we prove a large deviation principle for the empirical spectral distribution seen from the rightmost particle. This modified spectral distribution was introduced by Perret and Schehr (J. Stat. Phys. 2014) to study the crowding near the maximal eigenvalue, in the case of the GUE. We prove also convergence of fluctuations.

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Catherine Donati-Martin. Alain Rouault. "Near-extreme eigenvalues in the beta-ensembles." Electron. J. Probab. 21 1 - 17, 2016. https://doi.org/10.1214/16-EJP4

Information

Received: 2 February 2016; Accepted: 23 July 2016; Published: 2016
First available in Project Euclid: 25 August 2016

zbMATH: 1346.15034
MathSciNet: MR3546389
Digital Object Identifier: 10.1214/16-EJP4

Subjects:
Primary: 15B52, 60F10, 60G57

JOURNAL ARTICLE
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Vol.21 • 2016
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