Limiting behavior for the distance of a random walk.
Berestycki, Nathanael, Durrett, Rick (2008)
Electronic Journal of Probability [electronic only]
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Berestycki, Nathanael, Durrett, Rick (2008)
Electronic Journal of Probability [electronic only]
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Friedrich, Tobias, Sauerwald, Thomas (2010)
The Electronic Journal of Combinatorics [electronic only]
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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 . We prove that is bounded by a random constant...
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...
Harry Kesten (1986)
Annales de l'I.H.P. Probabilités et statistiques
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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...