
Random Walk Attracted by Percolation Clusters

Serguei Popov, Universidade de São Paulo, Brasil Marina Vachkovskaia, Universidade de Campinas, Brasil 
Abstract
Starting with a percolation model in Z^{d}
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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Published on: December 21, 2005

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