Pré-Publication, Document De Travail Année : 2013

Spectra of large diluted but bushy random graphs

Résumé

We compute an asymptotic expansion in $1/c$ of the limit in $n$ of the empirical spectral measure of the adjacency matrix of an Erd\H{o}s-Rényi random graph with $n$ vertices and parameter $c/n$. We present two different methods, one of which is valid for the more general setting of locally tree-like graphs. The second order in the expansion gives some information about the edge.

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Dates et versions

hal-00878739 , version 1 (30-10-2013)
hal-00878739 , version 2 (07-11-2013)

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Nathanael Enriquez, Laurent Menard. Spectra of large diluted but bushy random graphs. 2013. ⟨hal-00878739v2⟩
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