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.
Publié le : 2009-08-15
Classification:
Largest eigenvalues statistics,
Extreme values,
Random matrices,
Heavy tails,
15A52,
62G32,
60G55
@article{1249391376,
author = {Auffinger, Antonio and Ben Arous, G\'erard and P\'ech\'e, Sandrine},
title = {Poisson convergence for the largest eigenvalues of heavy tailed random matrices},
journal = {Ann. Inst. H. Poincar\'e Probab. Statist.},
volume = {45},
number = {1},
year = {2009},
pages = { 589-610},
language = {en},
url = {http://dml.mathdoc.fr/item/1249391376}
}
Auffinger, Antonio; Ben Arous, Gérard; Péché, Sandrine. Poisson convergence for the largest eigenvalues of heavy tailed random matrices. Ann. Inst. H. Poincaré Probab. Statist., Tome 45 (2009) no. 1, pp. 589-610. http://gdmltest.u-ga.fr/item/1249391376/