Poisson convergence for the largest eigenvalues of Heavy Tailed Random Matrices
Probability
2008-05-07 v3
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 \cite{Sos1}, we prove that, in the absence of the fourth moment, the top eigenvalues behave, in the limit, as the largest entries of the matrix.
Keywords
Cite
@article{arxiv.0710.3132,
title = {Poisson convergence for the largest eigenvalues of Heavy Tailed Random Matrices},
author = {Antonio Auffinger and Gerard Ben Arous and Sandrine Peche},
journal= {arXiv preprint arXiv:0710.3132},
year = {2008}
}
Comments
22 pages, to appear in Annales de l'Institut Henri Poincare