Electronic Journal of Probability

Return Probabilities of a Simple Random Walk on Percolation Clusters

Deborah Heicklen and Christopher Hoffman

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We bound the probability that a continuous time simple random walk on the infinite percolation cluster on $Z^d$ returns to the origin at time $t$. We use this result to show that in dimensions 5 and higher the uniform spanning forest on infinite percolation clusters supported on graphs with infinitely many connected components a.s.

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Electron. J. Probab., Volume 10 (2005), paper no. 8, 250-302.

Accepted: 4 March 2005
First available in Project Euclid: 1 June 2016

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Heicklen, Deborah; Hoffman, Christopher. Return Probabilities of a Simple Random Walk on Percolation Clusters. Electron. J. Probab. 10 (2005), paper no. 8, 250--302. doi:10.1214/EJP.v10-240. https://projecteuclid.org/euclid.ejp/1464816809

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