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arXiv · 1111.5492

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

Maria Shcherbina·Brunello Tirozzi
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Abstract

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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Maria Shcherbina, Brunello Tirozzi. 2011-11-23. Central limit theorem for fluctuations of linear eigenvalue statistics of large random graphs. Diluted regime. https://doi.org/10.1063/1.3698291

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