Resolvent of large random graphs

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Resolvent of large random graphs
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 Stieltjes transform of the spectral measure of such graphs. We illustrate our results on the uniform regular graphs, Erd¨os-R´enyi graphs and graphs with a given degree sequence. We give examples of application for weighted graphs, bipartite graphs and the uniform spanning tree of n vertices. MSC-class: 05C80, 15A52 (primary), 47A10 (secondary).
Charles Bordenave, Marc Lelarge
Added 30 Jan 2011
Updated 30 Jan 2011
Type Journal
Year 2010
Where RSA
Authors Charles Bordenave, Marc Lelarge
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