Random walk on the incipient infinite cluster on trees

Abstract

Let $\mathcal{G}$ be the incipient infinite cluster (IIC) for percolation on a homogeneous tree of degree $n_0 + 1$. We obtain estimates for the transition density of the continuous time simple random walk $Y$ on $\mathcal{G}$; the process satisfies anomalous diffusion and has spectral dimension 4/3.