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

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.

19 pages

References in corpus (2)

• Central limit theorem for linear eigenvalue statistics of random matrices with independent entries
• Central Limit Theorem for linear eigenvalue statistics of the Wigner and sample covariance random matrices

Cited by in corpus (4)

• Bulk universality of sparse random matrices
• Regularity conditions in the CLT for linear eigenvalue statistics of Wigner matrices
• On the correlation functions of the characteristic polynomials of the sparse hermitian random matrices
• Global eigenvalue fluctuations of random biregular bipartite graphs