Random walk on the incipient infinite cluster on trees

Martin T. Barlow, Takashi Kumagai

Published 2005-03-07Version 1

Let ${\cal G}$ 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 ${\cal G}$; the process satisfies anomalous diffusion and has spectral dimension 4/3.