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

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