Poisson convergence for the largest eigenvalues of heavy tailed random matrices

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. © 2009 Association des Publications de l'Institut Henri Poincaré.