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1 LPMA - Laboratoire de Probabilités et Modèles Aléatoires 2 MODAL-X - Modélisation aléatoire de Paris X 3 Modélisation aléatoire de Paris X MODAL-X - Modélisation aléatoire de Paris X

Abstract : 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.

Keywords : random matrices random graphs random trees adjacency matrix random matrices.





Author: Nathanael Enriquez - Laurent Menard -

Source: https://hal.archives-ouvertes.fr/



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