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Random Walk Delayed on Percolation Clusters

Part of: Applications to specific types of physical systems Limit theorems Special processes

Published online by Cambridge University Press:  14 July 2016

Francis Comets  and
François Simenhaus
Francis Comets*
Affiliation:
Université Paris Diderot - Paris 7
François Simenhaus*
Affiliation:
Université Paris Diderot - Paris 7
*
∗ Postal address: Université Paris Diderot - Paris 7, UFR de Mathématiques, Case 7012, 75205 Paris Cedex 13, France.
∗ Postal address: Université Paris Diderot - Paris 7, UFR de Mathématiques, Case 7012, 75205 Paris Cedex 13, France.
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Abstract

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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.

Keywords

Random walk in a random environmentsubcritical percolationanomalous transportanomalous diffusionenvironment seen from the particlecoupling

MSC classification

Secondary: 60K37: Processes in random environments 60F15: Strong theorems 60K35: Interacting random processes; statistical mechanics type models; percolation theory 82D30: Random media, disordered materials (including liquid crystals and spin glasses)

Information

Type
Research Article
Information
Journal of Applied Probability , Volume 45 , Issue 3 , September 2008 , pp. 689 - 702
Copyright
Copyright © Applied Probability Trust 2008 

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