Application of Moderate Deviation Techniques to Prove Sinai Theorem on RWRE
Abstract
We apply the techniques developed in Comets and Popov (Probab Theory Relat Fields 126:571-609, 2003) to present a new proof to Sinai theorem Sinai (Theory Probab Appl 27:256-268, 1982) on one-dimensional random walk in random environment (RWRE), working in a scale-free way to avoid rescaling arguments and splitting the proof in two independent parts: a quenched one, related to the measure conditioned on a fixed, typical realization of the environment, and an annealed one, related to the product measure of the environment . The quenched part still holds even if we use another measure (possibly dependent) for the environment.
- Publication:
-
Journal of Statistical Physics
- Pub Date:
- July 2015
- DOI:
- 10.1007/s10955-015-1266-1
- Bibcode:
- 2015JSP...160..357F