Central Limit Theorems for Linear Statistics of Heavy Tailed Random Matrices
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Guionnet_Central limit.pdf
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Author(s)
Benaych-Georges, Florent
Guionnet, Alice
Male, Camille
Date Issued
March 2014
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
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.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
https://doi.org/10.1007/s00220-014-1975-3
