Resolvent of Large Random Graphs

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We analyze the convergence of the spectrum of large random graphs to the spectrum of a limit infinite graph. We apply these results to graphs converging locally to trees and derive a new formula for the Stieljes transform of the spectral measure of such graphs. We illustrate our results on the uniform regular graphs, Erdos-Renyi graphs and preferential attachment graphs. We sketch examples of application for weighted graphs, bipartite graphs and the uniform spanning tree of n vertices.
21 pages, 1 figure

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Probability, Mathematical Physics, 05C80, 15A52 (Primary); 47A10 (Secondary)

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http://salesiana.dossiersoluciones.com/handle/123456789/229181

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0801.0155
 http://arxiv.org/abs/0801.0155

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arXiv