Large deviations for near-extreme eigenvalues in the beta-ensembles
Probability
2016-06-02 v2
Abstract
For beta ensembles with convex poynomial 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.
Cite
@article{arxiv.1512.00958,
title = {Large deviations for near-extreme eigenvalues in the beta-ensembles},
author = {Catherine Donati-Martin and Alain Rouault},
journal= {arXiv preprint arXiv:1512.00958},
year = {2016}
}
Comments
We fixed typos and changed Remarks 2.13 and 2.14