Poisson convergence for the largest eigenvalues of heavy tailed random matrices

Antonio Auffinger, Gerard 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 2009

Fingerprint

Sample Covariance Matrix
Largest Eigenvalue
Random Matrices
Siméon Denis Poisson
Asymptotic Behavior
Electron
Moment
Statistics
Eigenvalue
Eigenvalues
Asymptotic behavior
Covariance matrix

Keywords

  • Extreme values
  • Heavy tails
  • Largest eigenvalues statistics
  • Random matrices

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Cite this

Poisson convergence for the largest eigenvalues of heavy tailed random matrices. / Auffinger, Antonio; Ben Arous, Gerard; Péchéb, Sandrine.

In: Annales de l'institut Henri Poincare (B) Probability and Statistics, Vol. 45, No. 3, 08.2009, p. 589-610.

Research output: Contribution to journalArticle

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