Spectra of large diluted but bushy random graphs

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 of the spectrum. MSC 2010 Classification: 05C80; 60B20.