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A note on quenched moderate deviations for Sinai’s random walk in random environment. (English) Zbl 1171.60396
Summary: 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 \lbrace -\mathrm{Const}\cdot t^a / [(1-a)\ln t] (1+o(1))\rbrace $.

MSC:
60K37Processes in random environments
60F10Large deviations
82B41Random walks, random surfaces, lattice animals, etc. (statistical mechanics)
82B44Disordered systems (equilibrium statistical mechanics)
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References:
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