Spectral measures of random graphs
نویسنده
چکیده
These lecture notes are devoted to the spectral analysis of adjacency operators of graphs and random graphs. With the notion of unimodular random graphs, it is possible to define a natural notion of average spectral measure which corresponds to the density of states in the language of mathematical physics, to the Plancherel measure for Cayley graphs and, for finite graphs, to the empirical measure of the eigenvalues. We study the atoms and the regularity properties of this average spectral measure. We also present basic tools to address the problem of delocalization of the eigenvectors which is of prime importance in mathematical physics.
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تاریخ انتشار 2014