Electronic Journal of Probability
- Electron. J. Probab.
- Volume 21 (2016), paper no. 52, 17 pp.
Near-extreme eigenvalues in the beta-ensembles
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.
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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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