Poisson convergence for the largest eigenvalues of Heavy Tailed Random Matrices

Details Poisson convergence for the largest eigenvalues of Heavy Tailed Random Matrices Poisson convergence for the largest eigenvalues of Heavy Tailed Random Matrices

2007-10-16

arxiv.org/abs/0710.3132v3

Mathematics

Probability

22 pages, to appear in Annales de l'Institut Henri Poincare

Scientific paper

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.

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