{"paper":{"title":"Ergodicity of group actions and spectral gap, applications to random walks and Markov shifts","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Jean-Pierre Conze (IRMAR), Yves Guivarc'H (IRMAR)","submitted_at":"2011-06-16T14:52:43Z","abstract_excerpt":"Let $(X, \\cal B, \\nu)$ be a probability space and let $\\Gamma$ be a countable group of $\\nu$-preserving invertible maps of $X$ into itself. To a probability measure $\\mu$ on $\\Gamma$ corresponds a random walk on $X$ with Markov operator $P$ given by $P\\psi(x) = \\sum_{a} \\psi(ax) \\, \\mu(a)$. A powerful tool is the spectral gap property for the operator $P$ when it holds. We consider various examples of ergodic $\\Gamma$-actions and random walks and their extensions by a vector space: groups of automorphisms or affine transformations on compact nilmanifolds, random walk in random scenery on non a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.3248","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"}