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 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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