Scaling limit for the random walk on the largest connected component of the critical random graph

Abstract

A scaling limit for the simple random walk on the largest connected component of the Erdös-Rényi random graph G(n,p) in the critical window, p = n-1 + λn-4/3, is deduced. The limiting diffusion is constructed using resistance form techniques, and is shown to satisfy the same quenched short-time heat kernel asymptotics as the Brownian motion on the continuum random tree. © 2012 Research Institute for Mathematical Sciences, Kyoto University. All rights reserved.