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November 2018 On the large deviations of traces of random matrices
Fanny Augeri
Ann. Inst. H. Poincaré Probab. Statist. 54(4): 2239-2285 (November 2018). DOI: 10.1214/17-AIHP870

Abstract

We present large deviations principles for the moments of the empirical spectral measure of Wigner matrices and empirical measure of $\beta $-ensembles in three cases: the case of $\beta $-ensembles associated with a convex potential with polynomial growth, the case of Gaussian Wigner matrices, and the case of Wigner matrices without Gaussian tails, that is Wigner matrices whose entries have tail distributions decreasing as $e^{-ct^{\alpha }}$, for some constant $c>0$ and with $\alpha \in (0,2)$.

Nous proposons des principes de grandes déviations pour les moments de la mesure spectrale empirique de matrices de Wigner et de la mesure empirique de $\beta $-ensembles dans trois cas : celui des $\beta $-ensembles associés à un potentiel convexe à croissance polynomiale, le cas des matrices de Wigner Gaussiennes, et le cas des matrices de Wigner sans queues Gaussiennes, c’est-à-dire dont les entrées ont une queue de distribution ayant le même comportement que $e^{-ct^{\alpha }}$, pour une certaine constante $c>0$ et $\alpha \in (0,2)$.

Citation

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Fanny Augeri. "On the large deviations of traces of random matrices." Ann. Inst. H. Poincaré Probab. Statist. 54 (4) 2239 - 2285, November 2018. https://doi.org/10.1214/17-AIHP870

Information

Received: 23 May 2016; Revised: 6 September 2017; Accepted: 22 October 2017; Published: November 2018
First available in Project Euclid: 18 October 2018

zbMATH: 06996564
MathSciNet: MR3865672
Digital Object Identifier: 10.1214/17-AIHP870

Subjects:
Primary: 60B20
Secondary: 60F10

Keywords: $\beta $-ensembles , large deviations , Wigner matrices

Rights: Copyright © 2018 Institut Henri Poincaré

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Vol.54 • No. 4 • November 2018
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