Poisson convergence for the largest eigenvalues of Heavy Tailed Random Matrices

Antonio Auffinger; Gerard Ben Arous; Sandrine Peche

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arXiv · 0710.3132

Poisson convergence for the largest eigenvalues of Heavy Tailed Random Matrices

Antonio Auffinger·Gerard Ben Arous·Sandrine Peche

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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.

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Antonio Auffinger, Gerard Ben Arous, Sandrine Peche. 2008-05-07. Poisson convergence for the largest eigenvalues of Heavy Tailed Random Matrices. https://arxiv.org/abs/0710.3132

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