Resolvent of Large Random Graphs

Details Resolvent of Large Random Graphs Resolvent of Large Random Graphs

2007-12-31

arxiv.org/abs/0801.0155v3

Mathematics

Probability

21 pages, 1 figure

Scientific paper

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.

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