IDLA on the Supercritical Percolation Cluster

Eric Shellef (Weizmann Institute of Science)

Abstract


We consider the internal diffusion limited aggregation (IDLA) process on the infinite cluster in supercritical Bernoulli bond percolation on $\mathbb{Z}^d$. It is shown that the process on the cluster behaves like it does on the Euclidean lattice, in that the aggregate covers all the vertices in a Euclidean ball around the origin, such that the ratio of vertices in this ball to the total number of particles sent out approaches one almost surely.

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Pages: 723-740

Publication Date: May 24, 2010

DOI: 10.1214/EJP.v15-775

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