Random walk delayed on percolation clusters
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
TypeArticle accepté pour publication ou publié
External document linkhttp://arxiv.org/abs/0710.2320v1
Journal nameJournal of Applied Probability
Applied Probability Trust
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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 / KeywordsRandom walk in a random environment; subcritical percolation; anomalous transport; anomalous diffusion; environment seen from the particle; coupling
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