Spectra of large diluted but bushy random graphs

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 Erdős-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.

24 pages, 5 figures

References in corpus (1)

• The rank of diluted random graphs

Cited by in corpus (1)

• Global eigenvalue fluctuations of random biregular bipartite graphs