Central limit theorem for fluctuations of linear eigenvalue statistics of large random graphs. Diluted regime

Maria Shcherbina, Brunello Tirozzi

Published 2011-11-23Version 1

We study the linear eigenvalue statistics of large random graphs in the regimes when the mean number of edges for each vertex tends to infinity. We prove that for a rather wide class of test functions the fluctuations of linear eigenvalue statistics converges in distribution to a Gaussian random variable with zero mean and variance which coincides with "non gaussian" part of the Wigner ensemble variance.