Electronic Journal of Probability

Near-extreme eigenvalues in the beta-ensembles

Catherine Donati-Martin and Alain Rouault

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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.

Article information

Electron. J. Probab., Volume 21 (2016), paper no. 52, 17 pp.

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

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Zentralblatt MATH identifier

Primary: 15B52: Random matrices 60G57: Random measures 60F10: Large deviations

beta-ensembles spectral distribution top eigenvalue large deviations

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Donati-Martin, Catherine; Rouault, Alain. Near-extreme eigenvalues in the beta-ensembles. Electron. J. Probab. 21 (2016), paper no. 52, 17 pp. doi:10.1214/16-EJP4. https://projecteuclid.org/euclid.ejp/1472142775

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