{"paper":{"title":"An Almost Sure Invariance Principle for Several Classes of Random Dynamical Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Jason Atnip","submitted_at":"2017-02-24T18:20:28Z","abstract_excerpt":"In this paper we deal with a large class of dynamical systems having a version of the spectral gap property. Our primary class of systems comes from random dynamics, but we also deal with the deterministic case. We show that if a random dynamical system has a fiberwise spectral gap property as well as an exponential decay of correlations in the base, then, developing on Gou\\\"{e}zel's approach, the system satisfies the almost sure invariance principle. The result is then applied to uniformly expanding random systems like those studied by Denker and Gordin and Mayer, Skorulski, and Urba\\'nski."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.07691","kind":"arxiv","version":2},"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"}