Cavity and replica methods for the spectral density of sparse symmetric random matrices
Cavity and replica methods for the spectral density of sparse symmetric random matrices
We review the problem of how to compute the spectral density of sparse symmetric random matrices, i.e. weighted adjacency matrices of undirected graphs. Starting from the Edwards-Jones formula, we illustrate the milestones of this line of research, including the pioneering work of Bray and Rodgers using replicas. We focus first …