Random walk delayed on percolation clusters

Simenhaus, François; Comets, Francis

Simenhaus, François; Comets, Francis (2008), Random walk delayed on percolation clusters, Journal of Applied Probability, 45, 3, p. 689-702. http://dx.doi.org/10.1239/jap/1222441823

Type

Article accepté pour publication ou publié

External document link

http://arxiv.org/abs/0710.2320v1

Date

2008

Journal name

Journal of Applied Probability

Volume

Number

Publisher

Applied Probability Trust

Pages

689-702

Abstract (EN)

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.

Subjects / Keywords

Random walk in a random environment; subcritical percolation; anomalous transport; anomalous diffusion; environment seen from the particle; coupling