Random Walk Delayed on Percolation Cluster

Francis Comets (1) , François Simenhaus (1)

1 LPMA - Laboratoire de Probabilités et Modèles Aléatoires

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.

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

Domaines: Probabilités [math.PR]

Francis Comets, François Simenhaus. Random Walk Delayed on Percolation Cluster. Journal of Applied Probability, 2008, 45 (3), pp.689-702. ⟨10.1239/jap/1222441823⟩. ⟨hal-00656007⟩