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Displaying similar documents to “Maximal displacement for bridges of random walks in a random environment”

Large deviations for transient random walks in random environment on a Galton–Watson tree

Elie Aidékon (2010)

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

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Consider a random walk in random environment on a supercritical Galton–Watson tree, and let be the hitting time of generation . The paper presents a large deviation principle for /, both in quenched and annealed cases. Then we investigate the subexponential situation, revealing a polynomial regime similar to the one encountered in one dimension. The paper heavily relies on estimates on the tail distribution of the first regeneration time.

A note on quenched moderate deviations for Sinai’s random walk in random environment

Francis Comets, Serguei Popov (2004)

ESAIM: Probability and Statistics

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We consider the continuous time, one-dimensional random walk in random environment in Sinai’s regime. We show that the probability for the particle to be, at time t and in a typical environment, at a distance larger than t a ( 0 < a < 1 ) from its initial position, is exp { - Const · t a / [ ( 1 - a ) ln t ] ( 1 + o ( 1 ) ) } .

A note on quenched moderate deviations for Sinai's random walk in random environment

Francis Comets, Serguei Popov (2010)

ESAIM: Probability and Statistics

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We consider the continuous time, one-dimensional random walk in random environment in Sinai's regime. We show that the probability for the particle to be, at time and in a typical environment, at a distance larger than () from its initial position, is exp{-Const ⋅ ln(1))}.

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...

Windings of planar random walks and averaged Dehn function

Bruno Schapira, Robert Young (2011)

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

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We prove sharp estimates on the expected number of windings of a simple random walk on the square or triangular lattice. This gives new lower bounds on the averaged Dehn function, which measures the expected area needed to fill a random curve with a disc.