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 Electronic Communications in Probability > Vol. 10 (2005) > Paper 27 open journal systems 

Random Walk Attracted by Percolation Clusters

Serguei Popov, Universidade de São Paulo, Brasil
Marina Vachkovskaia, Universidade de Campinas, Brasil

Starting with a percolation model in Zd in the subcritical regime, we consider a random walk described as follows: the probability of transition from x to y is proportional to some function f of the size of the cluster of y. This function is supposed to be increasing, so that the random walk is attracted by bigger clusters. For f(t)=e βt we prove that there is a phase transition in β, i.e., the random walk is subdiffusive for large β and is diffusive for small β.

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Pages: 263-272

Published on: December 21, 2005

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Electronic Communications in Probability. ISSN: 1083-589X