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

Amir Dembo; Alice Guionnet; Ofer Zeitouni

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

Probability 2009-09-25 v1

Authors: Amir Dembo , Alice Guionnet , Ofer Zeitouni

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

Keywords

sinai model random walk in random environment aging annealed law rwre

Cite

@article{arxiv.math/0105215,
  title  = {Aging properties of Sinai's model of random walk in random environment},
  author = {Amir Dembo and Alice Guionnet and Ofer Zeitouni},
  journal= {arXiv preprint arXiv:math/0105215},
  year   = {2009}
}

Comments

This note will be part of the forthcoming lecture notes of O. Zeitouni on RWRE, to appear as proceedings of the St Flour summer school 2001

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

Abstract

Keywords

Cite

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