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moderate deviations.

ESAIM: Probability and Statistics (1)

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A note on quenched moderate deviations for Sinai's random walk in random environment
Francis Comets, Serguei Popov
Journal:

ESAIM: Probability and Statistics / Volume 8 / August 2004

Published online by Cambridge University Press:

15 September 2004, pp. 56-65

Print publication:

August 2004
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We consider the continuous time, one-dimensional random walk in random environmentin Sinai's regime. We show that the probability for theparticle 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))}.