Displaying similar documents to “Large deviations for transient random walks in random environment on a Galton–Watson tree”

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...

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 ) ) } .

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.

Large deviations for partition functions of directed polymers in an IID field

Iddo Ben-Ari (2009)

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

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Consider the partition function of a directed polymer in ℤ, ≥1, in an IID field. We assume that both tails of the negative and the positive part of the field are at least as light as exponential. It is well known that the free energy of the polymer is equal to a deterministic constant for almost every realization of the field and that the upper tail of the large deviations is exponential. The lower tail of the large deviations is typically lighter than exponential. In this paper we obtain...