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Central limit theorem for linear eigenvalue statistics of diluted random matrices

Connections for Women: An Introduction to Random Matrices September 20, 2010 - September 21, 2010

September 21, 2010 (03:30pm PDT - 04:30pm PDT)

Speaker(s): Mariya Shcherbyna

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Abstract

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

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