Near-extreme eigenvalues in the beta-ensembles

DOI10.1214/16-EJP4zbMATH Open1346.15034arXiv1512.00958OpenAlexW2510860759MaRDI QIDQ320211

Catherine Donati-Martin, Alain Rouault

Publication date: 6 October 2016

Published in: Electronic Journal of Probability (Search for Journal in Brave)

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.

Full work available at URL: https://arxiv.org/abs/1512.00958

zbMATH Keywords

large deviationsspectral distributionbeta-ensemblestop eigenvalue

Mathematics Subject Classification ID

Large deviations (60F10) Random measures (60G57) Random matrices (algebraic aspects) (15B52)

Related Items (1)

Strong approximation of Gaussian \(\beta\) ensemble characteristic polynomials: the hyperbolic regime

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