Journal of Statistical Physics

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

Application of Moderate Deviation Techniques to Prove Sinai Theorem on RWRE



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.


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

Mathematics Subject Classification

60K37 60G50 



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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