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

Amir Dembo·Alice Guionnet·Ofer Zeitouni
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Abstract

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: $$\lim_{η\to0} \lim_{n\to\infty} \PP^o (\frac{|X_{n^h} - X_n|}{(\log n)^2} < η) = \frac{1}{h^2} [ {5/3} - {2/3} e^{-(h-1)} ]. $$

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Amir Dembo, Alice Guionnet, Ofer Zeitouni. 2001-05-25. Aging properties of Sinai's model of random walk in random environment. https://arxiv.org/abs/math/0105215

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