Journal
ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES
Volume 45, Issue 3, Pages 589-610Publisher
INST MATHEMATICAL STATISTICS
DOI: 10.1214/08-AIHP188
Keywords
Largest eigenvalues statistics; Extreme values; Random matrices; Heavy tails
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Funding
- NSF [OISE-0730136]
- Direct For Mathematical & Physical Scien
- Division Of Mathematical Sciences [0806180] Funding Source: National Science Foundation
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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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