Poisson convergence for the largest eigenvalues of heavy tailed random matrices

Antonio Auffinger; Gérard Ben Arous; Sandrine Péchéb

doi:10.1214/08-AIHP188

Poisson convergence for the largest eigenvalues of heavy tailed random matrices

Antonio Auffinger, Gérard Ben Arous, Sandrine Péchéb

Mathematics

Research output: Contribution to journal › Article › peer-review

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.

Original language	English (US)
Pages (from-to)	589-610
Number of pages	22
Journal	Annales de l'institut Henri Poincare (B) Probability and Statistics
Volume	45
Issue number	3
DOIs	https://doi.org/10.1214/08-AIHP188
State	Published - Aug 2009

Keywords

Extreme values
Heavy tails
Largest eigenvalues statistics
Random matrices

ASJC Scopus subject areas

Statistics and Probability
Statistics, Probability and Uncertainty

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10.1214/08-AIHP188

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AU - Arous, Gérard Ben

AU - Péchéb, Sandrine

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AB - 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.

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KW - Heavy tails

KW - Largest eigenvalues statistics

KW - Random matrices

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Poisson convergence for the largest eigenvalues of heavy tailed random matrices

Abstract

Keywords

ASJC Scopus subject areas

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