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2010 IDLA on the Supercritical Percolation Cluster
Eric Shellef
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Electron. J. Probab. 15: 723-740 (2010). DOI: 10.1214/EJP.v15-775

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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Eric Shellef. "IDLA on the Supercritical Percolation Cluster." Electron. J. Probab. 15 723 - 740, 2010. https://doi.org/10.1214/EJP.v15-775

Information

Accepted: 24 May 2010; Published: 2010
First available in Project Euclid: 1 June 2016

zbMATH: 1226.60136
MathSciNet: MR2650780
Digital Object Identifier: 10.1214/EJP.v15-775

Subjects:
Primary: 60K35

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Vol.15 • 2010
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