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

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

2011-11-23

arxiv.org/abs/1111.5492v1

Physics

Mathematical Physics

19 pages

Scientific paper

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.

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