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Central Limit Theorems for Linear Statistics of Heavy Tailed Random Matrices

Author(s)
Benaych-Georges, Florent; Guionnet, Alice; Male, Camille
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Abstract
We show central limit theorems (CLT) for the linear statistics of symmetric matrices with independent heavy tailed entries, including entries in the domain of attraction of α-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 the case of standard Wigner matrices, the normalization is the one of the classical CLT for independent random variables.
Date issued
2014-03
URI
http://hdl.handle.net/1721.1/92885
Department
Massachusetts Institute of Technology. Department of Mathematics
Journal
Communications in Mathematical Physics
Publisher
Springer-Verlag Berlin Heidelberg
Citation
Benaych-Georges, Florent, Alice Guionnet, and Camille Male. “Central Limit Theorems for Linear Statistics of Heavy Tailed Random Matrices.” Commun. Math. Phys. 329, no. 2 (March 16, 2014): 641–686.
Version: Author's final manuscript
ISSN
0010-3616
1432-0916

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