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2005 Return Probabilities of a Simple Random Walk on Percolation Clusters
Deborah Heicklen, Christopher Hoffman
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Electron. J. Probab. 10(none): 250-302 (2005). DOI: 10.1214/EJP.v10-240

Abstract

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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Deborah Heicklen. Christopher Hoffman. "Return Probabilities of a Simple Random Walk on Percolation Clusters." Electron. J. Probab. 10 250 - 302, 2005. https://doi.org/10.1214/EJP.v10-240

Information

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

zbMATH: 1070.60067
MathSciNet: MR2120245
Digital Object Identifier: 10.1214/EJP.v10-240

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