Delocalization Transition for Critical Erdős–Rényi Graphs
Delocalization Transition for Critical Erdős–Rényi Graphs
We analyse the eigenvectors of the adjacency matrix of a critical Erdős-Rényi graph G(N,d/N) , where d is of order logN . We show that its spectrum splits into two phases: a delocalized phase in the middle of the spectrum, where the eigenvectors are completely delocalized, and a semilocalized phase …