Return Probabilities of a Simple Random Walk on Percolation Clusters
Authors:
Open Access
- 1 January 2005
- journal article
- Published by Institute of Mathematical Statistics in Electronic Journal of Probability
- Vol. 10 (none) , 250-302
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.
Keywords
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