Reversed Dirichlet environment and directional transience of random walks in Dirichlet environment

Christophe Sabot; Laurent Tournier

Displaying similar documents to “Reversed Dirichlet environment and directional transience of random walks in Dirichlet environment”

Giant vacant component left by a random walk in a random d-regular graph

Jiří Černý, Augusto Teixeira, David Windisch (2011)

Annales de l'I.H.P. Probabilités et statistiques

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We study the trajectory of a simple random walk on a -regular graph with ≥ 3 and locally tree-like structure as the number of vertices grows. Examples of such graphs include random -regular graphs and large girth expanders. For these graphs, we investigate percolative properties of the set of vertices not visited by the walk until time , where > 0 is a fixed positive parameter. We show that this so-called set exhibits a phase transition in in the following sense: there exists...

Anomalous heat-kernel decay for random walk among bounded random conductances

N. Berger, M. Biskup, C. E. Hoffman, G. Kozma (2008)

Annales de l'I.H.P. Probabilités et statistiques

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We consider the nearest-neighbor simple random walk on ℤ, ≥2, driven by a field of bounded random conductances ∈[0, 1]. The conductance law is i.i.d. subject to the condition that the probability of >0 exceeds the threshold for bond percolation on ℤ. For environments in which the origin is connected to infinity by bonds with positive conductances, we study the decay of the 2-step return probability $𝖯_{ω}^{2 n} (0, 0)$ . We prove that $𝖯_{ω}^{2 n} (0, 0)$ is bounded by a random constant...

Connectivity bounds for the vacant set of random interlacements

Vladas Sidoravicius, Alain-Sol Sznitman (2010)

Annales de l'I.H.P. Probabilités et statistiques

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The model of random interlacements on ℤ, ≥3, was recently introduced in [Vacant set of random interlacements and percolation. Available at http://www.math.ethz.ch/u/sznitman/preprints]. A non-negative parameter parametrizes the density of random interlacements on ℤ. In the present note we investigate connectivity properties of the vacant set left by random interlacements at level , in the non-percolative regime >∗, with ∗ the non-degenerate critical parameter for the percolation...

Uniqueness of the mixing measure for a random walk in a random environment on the positive integers.

Eckhoff, Maren, Rolles, Silke W.W. (2009)

Electronic Communications in Probability [electronic only]

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Limit theorem for random walk in weakly dependent random scenery

Nadine Guillotin-Plantard, Clémentine Prieur (2010)

Annales de l'I.H.P. Probabilités et statistiques

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Let =( )≥0 be a random walk on ℤ and =( )∈ℤ a stationary random sequence of centered random variables, independent of . We consider a random walk in random scenery that is the sequence of random variables ( )≥0, where =∑=0 , ∈ℕ. Under a weak dependence assumption on the scenery we prove a functional limit theorem generalizing Kesten and Spitzer’s [ (1979) 5–25]...

Scaling limit of the random walk among random traps on ℤd

Jean-Christophe Mourrat (2011)

Annales de l'I.H.P. Probabilités et statistiques

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Attributing a positive value to each ∈ℤ, we investigate a nearest-neighbour random walk which is reversible for the measure with weights ( ), often known as “Bouchaud’s trap model.” We assume that these weights are independent, identically distributed and non-integrable random variables (with polynomial tail), and that ≥5. We obtain the quenched subdiffusive scaling limit of the model, the limit being the fractional kinetics process. We begin our proof...