Poisson convergence for the largest eigenvalues of heavy tailed random matrices

Antonio Auffinger, Gérard Ben Arous, Sandrine Péchéb

Research output: Contribution to journalArticle

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 languageEnglish (US)
Pages (from-to)589-610
Number of pages22
JournalAnnales de l'institut Henri Poincare (B) Probability and Statistics
Volume45
Issue number3
DOIs
StatePublished - Aug 1 2009

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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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