Aging properties of Sinai's model of random walk in random environment

Details Aging properties of Sinai's model of random walk in random environment Aging properties of Sinai's model of random walk in random environment

2001-05-25

arxiv.org/abs/math/0105215v1

Mathematics

Probability

This note will be part of the forthcoming lecture notes of O. Zeitouni on RWRE, to appear as proceedings of the St Flour summe

Scientific paper

We study in this short note aging properties of Sinai's (nearest neighbour) random walk in random environment. With $\PP^o$ denoting the annealed law of the RWRE $X_n$, our main result is a full proof of the following statement due to P. Le Doussal, C. Monthus and D. S. Fisher: $$\lim_{\eta\to0} \lim_{n\to\infty} \PP^o (\frac{|X_{n^h} - X_n|}{(\log n)^2} < \eta) = \frac{1}{h^2} [ {5/3} - {2/3} e^{-(h-1)} ]. $$

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