Localized phase for the Erdős-Rényi graph

Johannes Alt, Raphael Ducatez, Antti Knowles

We analyse the eigenvectors of the adjacency matrix of the Erdős-Rényi graph $\mathbb{G}(N,d/N)$ for $\sqrt{\log N}\ll d\lesssim \log N$. We show the existence of a localized phas…