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 Electronic Journal of Probability > Vol. 10 (2005) > Paper 8 open journal systems 


Return Probabilities of a Simple Random Walk on Percolation Clusters

Deborah Heicklen, Lockhead-Martin, USA
Christopher Hoffman, University of Washington, USA


Abstract
We bound the probability that a continuous time simple random walk on the infinite percolation cluster on Zd 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.


Full text: PDF

Pages: 250-302

Published on: March 4, 2005
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Electronic Journal of Probability. ISSN: 1083-6489