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. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.3698291]
Central limit theorem for fluctuations of linear eigenvalue statistics of large random graphs: Diluted regime / Mariya, Shcherbina; Tirozzi, Benedetto. - In: JOURNAL OF MATHEMATICAL PHYSICS. - ISSN 0022-2488. - STAMPA. - 53:4(2012), pp. 043501-043501-18. [10.1063/1.3698291]
Central limit theorem for fluctuations of linear eigenvalue statistics of large random graphs: Diluted regime
TIROZZI, Benedetto
2012
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. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.3698291]I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
