Poisson convergence for the largest eigenvalues of heavy tailed random matrices
Antonio Auffinger, Gérard Ben Arous, and Sandrine Péché
Source: Ann. Inst. H. Poincaré Probab. Statist. Volume 45, Number 3
(2009), 589-610.
Abstract
We study the statistics of the largest eigenvalues of real symmetric and sample covariance matrices when the entries are heavy tailed. Extending the result obtained by Soshnikov in (Electron. Commun. Probab. 9 (2004) 82–91), we prove that, in the absence of the fourth moment, the asymptotic behavior of the top eigenvalues is determined by the behavior of the largest entries of the matrix.
Résumé
On étudie la loi des plus grandes valeurs propres de matrices aléatoires symétriques réelles et de covariance empirique quand les coefficients des matrices sont à queue lourde. On étend le résultat obtenu par Soshnikov dans (Electron. Commun. Probab. 9 (2004) 82–91) et on montre que le comportement asymptotique des plus grandes valeurs propres est déterminé par les plus grandes entrées de la matrice.
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Permanent link to this document: http://projecteuclid.org/euclid.aihp/1249391376
Digital Object Identifier: doi:10.1214/08-AIHP188
Zentralblatt MATH identifier: 05611480
Mathematical Reviews number (MathSciNet): MR2548495
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Annales de l'Institut Henri Poincaré, Probabilités et Statistiques
