Central limit theorems for linear statistics of heavy tailed random matrices

Abstract : We show central limit theorems (CLT) for the Stieltjes transforms or more general analytic functions of symmetric matrices with independent heavy tailed entries, including entries in the domain of attraction of $\alpha$-stable laws and entries with moments exploding with the dimension, as in the adjacency matrices of Erdös-Rényi graphs. For the second model, we also prove a central limit theorem of the moments of its empirical eigenvalues distribution. The limit laws are Gaussian, but unlike to the case of standard Wigner matrices, the normalization is the one of the classical CLT for independent random variables.
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Communications in Mathematical Physics, Springer Verlag, 2014, 239 (2), pp.641-686. <10.1007/s00220-014-1975-3>
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Contributeur : Florent Benaych-Georges <>
Soumis le : mercredi 25 décembre 2013 - 19:23:53
Dernière modification le : jeudi 27 avril 2017 - 09:46:42
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Florent Benaych-Georges, Alice Guionnet, Camille Male. Central limit theorems for linear statistics of heavy tailed random matrices. Communications in Mathematical Physics, Springer Verlag, 2014, 239 (2), pp.641-686. <10.1007/s00220-014-1975-3>. <hal-00769741v5>

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