Delocalization and limiting spectral distribution of Erdos-Renyi graphs with constant expected degree

Abstract

For fixed lambda > 0, it is known that Erdos-Renyi graphs {G(n, lambda/n), n is an element of N}, with edge-weights 1/root lambda, have a limiting spectral distribution, nu(lambda). As lambda -> infinity {nu(lambda)} converges to the semicircle distribution. For large A, we find an orthonormal eigenvector basis of G(n, lambda/n) where most of the eigenvectors have small infinity norms as n -> infinity providing a variant of an eigenvector delocalization result of Tran, Vu, and Wang (2013).