Annales de l'Institut Henri Poincaré, Probabilités et Statistiques

On the large deviations of traces of random matrices

Fanny Augeri

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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 $\alpha \in (0,2)$.

Résumé

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 $\alpha \in (0,2)$.

Article information

Source
Ann. Inst. H. Poincaré Probab. Statist., Volume 54, Number 4 (2018), 2239-2285.

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

Permanent link to this document
https://projecteuclid.org/euclid.aihp/1539849798

Digital Object Identifier
doi:10.1214/17-AIHP870

Mathematical Reviews number (MathSciNet)
MR3865672

Zentralblatt MATH identifier
06996564

Subjects
Primary: 60B20: Random matrices (probabilistic aspects; for algebraic aspects see 15B52)
Secondary: 60F10: Large deviations

Keywords
Large deviations Wigner matrices $\beta $-ensembles

Citation

Augeri, Fanny. On the large deviations of traces of random matrices. Ann. Inst. H. Poincaré Probab. Statist. 54 (2018), no. 4, 2239--2285. doi:10.1214/17-AIHP870. https://projecteuclid.org/euclid.aihp/1539849798


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