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Journal of Statistical Physics

, Volume 160, Issue 2, pp 357–370 | Cite as

Application of Moderate Deviation Techniques to Prove Sinai Theorem on RWRE

  • Marcelo Ventura Freire
Article

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 \(P_{\omega }\) conditioned on a fixed, typical realization \(\omega \) of the environment, and an annealed one, related to the product measure \(\mathbb {P}\) of the environment \(\omega \). The quenched part still holds even if we use another measure (possibly dependent) for the environment.

Keywords

Random walk Random environment Sinai walk Moderate deviations Metastability \(t\)-Stable point 

Mathematics Subject Classification

60K37 60G50 

Notes

Acknowledgments

The author wishes to express his gratitude to both reviewers for their valuable suggestions.

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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Escola de Artes, Ciências e HumanidadesUniversidade de São Paulo (EACHUSP)São PauloBrazil

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