Local law and complete eigenvector delocalization for supercritical Erdős-Rényi graphs

Yukun He, Antti Knowles, Matteo Marcozzi

We prove a local law for the adjacency matrix of the Erdős-Rényi graph $G(N,p)$ in the supercritical regime $pN\ge C\log N$ where $G(N,p)$ has with high probability no isolated…