{"paper":{"title":"Application of moderate deviation techniques to prove Sinai's Theorem on RWRE","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Marcelo Ventura Freire","submitted_at":"2014-03-28T20:29:08Z","abstract_excerpt":"We apply the techniques developed in Comets and Popov (2003) to present a new proof to Sinai's theorem (Sinai, 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 environm"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.7535","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}