## Electronic Journal of Probability

### Return Probabilities of a Simple Random Walk on Percolation Clusters

#### 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.

#### Article information

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

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

https://projecteuclid.org/euclid.ejp/1464816809

Digital Object Identifier
doi:10.1214/EJP.v10-240

Mathematical Reviews number (MathSciNet)
MR2120245

Zentralblatt MATH identifier
1070.60067

Rights

#### Citation

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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