IDLA on the Supercritical Percolation Cluster
arXiv:0806.4771
Abstract
We consider the internal diffusion limited aggregation (IDLA) process on the infinite cluster in supercritical Bernoulli bond percolation on Euclidean lattices. 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.
17 pages, 1 figure - assumption of Gaussian estimates on graph relaxed to a nonuniform elliptic Harnack Inequality