Displaying similar documents to “A note on quenched moderate deviations for Sinai’s random walk in 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.

Maximal displacement for bridges of random walks in a random environment

Nina Gantert, Jonathon Peterson (2011)

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

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It is well known that the distribution of simple random walks on ℤ conditioned on returning to the origin after 2 steps does not depend on =(1=1), the probability of moving to the right. Moreover, conditioned on {2=0} the maximal displacement max≤2| | converges in distribution when scaled by √ (diffusive scaling). We consider the analogous problem for transient random walks in random environments on ℤ. We show that under the quenched law (conditioned on...

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.