Aging properties of Sinai's model of random walk in random environment
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_{\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)} ].