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arXiv · 1512.00958

Large deviations for near-extreme eigenvalues in the beta-ensembles

Catherine Donati-Martin·Alain Rouault
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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.

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Catherine Donati-Martin, Alain Rouault. 2016-06-01. Large deviations for near-extreme eigenvalues in the beta-ensembles. https://arxiv.org/abs/1512.00958

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