Central Limit Theorems for Linear Statistics of Heavy Tailed Random Matrices
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 αstable laws and entries with moments exploding with the dimension, as in the adjacency matrices of ErdösRényi 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.
 Publication:

Communications in Mathematical Physics
 Pub Date:
 July 2014
 DOI:
 10.1007/s0022001419753
 arXiv:
 arXiv:1301.0448
 Bibcode:
 2014CMaPh.329..641B
 Keywords:

 Mathematics  Probability
 EPrint:
 49 pages. In this fifth version, we have corrected a mistake in the fixed point equations for the limit covariance. To appear in Comm. Math. Phys