ABSTRACT

I discuss the fluctuations of individual eigenvalues of the adjacency matrix of the Erdos-Renyi graph $G(N,p)$.I show that if $N^{-1}\11 p \\11 N^{-2/3},then all nontrivial eigenvalues away from 0 have asymptotically Gaussian fluctuations. These fluctuations are governed by a single random variable, which has the interpretation of the total degree of the graph. Part of the result is a joint work with Antti Knowles.

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