A note on random walk in random scenery
Amine Asselah, Fabienne Castell (2007)
Annales de l'I.H.P. Probabilités et statistiques
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Amine Asselah, Fabienne Castell (2007)
Annales de l'I.H.P. Probabilités et statistiques
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Atilla Yilmaz (2010)
Annales de l'I.H.P. Probabilités et statistiques
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In his 2003 paper, Varadhan proves the averaged large deviation principle for the mean velocity of a particle taking a nearest-neighbor random walk in a uniformly elliptic i.i.d. environment on ℤ with ≥1, and gives a variational formula for the corresponding rate function . Under Sznitman’s transience condition (), we show that is strictly convex and analytic on a non-empty open set , and that the true velocity of the particle is an element (resp. in...
Tom Schmitz (2006)
Annales de l'I.H.P. Probabilités et statistiques
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Tomasz Komorowski, Grzegorz Krupa (2003)
Annales de l'I.H.P. Probabilités et statistiques
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Nina Gantert, Yueyun Hu, Zhan Shi (2011)
Annales de l'I.H.P. Probabilités et statistiques
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Consider a discrete-time one-dimensional supercritical branching random walk. We study the probability that there exists an infinite ray in the branching random walk that always lies above the line of slope − , where denotes the asymptotic speed of the right-most position in the branching random walk. Under mild general assumptions upon the distribution of the branching random walk, we prove that when → 0, this probability decays like exp{−(+o(1)) / 1/2}, where is a positive constant...
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...