Electronic Journal of Probability

Near-extreme eigenvalues in the beta-ensembles

Catherine Donati-Martin and Alain Rouault

Full-text: Open access

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.

Article information

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

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

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1472142775

Digital Object Identifier
doi:10.1214/16-EJP4

Mathematical Reviews number (MathSciNet)
MR3546389

Zentralblatt MATH identifier
1346.15034

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

Keywords
beta-ensembles spectral distribution top eigenvalue large deviations

Rights
Creative Commons Attribution 4.0 International License.

Citation

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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