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 Erdos-Renyi random graph in the critical window 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.

References in corpus (2)

• The Alexander-Orbach conjecture holds in high dimensions
• Critical random graphs: Diameter and mixing time