Random Walk on The Incipient Infinite Cluster on Trees

Abstract

Let script G sign be the incipient infinite cluster (IIC) for percolation on a homogeneous tree of degree n0 + 1. We obtain estimates for the transition density of the continuous time simple random walk Y on script G sign; the process satisfies anomalous diffusion and has spectral dimension 4/3. © 2006 University of Illinois.