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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

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
45
Number
3
Publisher
Applied Probability Trust
Pages
689-702
Publication identifier
Metadata
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Author(s)
Simenhaus, François
Comets, Francis
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