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

Francis Comets, Serguei Popov (2004)

ESAIM: Probability and Statistics

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 $exp {- Const \cdot t^{a} / [(1 - a) ln t] (1 + o (1))}$ .

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

Francis Comets, Serguei Popov (2010)

ESAIM: Probability and Statistics

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 ta (0<a<1) from its initial position, is exp{-Const ⋅ ta/[(1 - a)lnt](1 + o(1))}.

A remark concerning random walks with random potentials

Yakov Sinai (1995)

Fundamenta Mathematicae

We consider random walks where each path is equipped with a random weight which is stationary and independent in space and time. We show that under some assumptions the arising probability distributions are in a sense uniformly absolutely continuous with respect to the usual probability distribution for symmetric random walks.

An extension of the inductive approach to the lace expansion.

Holmes, Mark P., Van Der Hofstad, Remco, Slade, Gordon (2008)

Electronic Communications in Probability [electronic only]

Asymptotics for random walks in alcoves of affine Weyl groups.

Krattenthaler, Christian (2004)

Séminaire Lotharingien de Combinatoire [electronic only]