Return probability on Bienaymé-Galton-Watson trees and spectral asymptotics of sparse Erdős-Rényi random graphs

Markus Heydenreich, Peter Müller, Sara Terveer

We derive an upper bound for the annealed return probability of the simple random walk on supercritical Bienaymé-Galton-Watson trees. The bound decays subexponentially in time $t$…