Random walk delayed on percolation clusters

Details Random walk delayed on percolation clusters Random walk delayed on percolation clusters

2007-10-11

arxiv.org/abs/0710.2320v1

Mathematics

Probability

Scientific paper

We study a continuous time random walk on the $d$-dimensional lattice, subject to a drift and an attraction to large clusters of a subcritical Bernoulli site percolation. We find two distinct regimes: a ballistic one, and a subballistic one taking place when the attraction is strong enough. We identify the speed in the former case, and the algebraic rate of escape in the latter case. Finally, we discuss the diffusive behavior in the case of zero drift and weak attraction.

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