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IDLA on the Supercritical Percolation Cluster
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Eric Shellef, Weizmann Institute of Science
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Abstract
Abstract. We consider the internal diffusion limited aggregation (IDLA) process on the infinite cluster in supercritical Bernoulli bond percolation on 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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Full text: PDF
Pages: 723-740
Published on: May 24, 2010
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Electronic Journal of Probability. ISSN: 1083-6489 |
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