{"paper":{"title":"Generic Stationary Measures and Actions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.GR","authors_text":"Lewis Bowen, Omer Tamuz, Yair Hartman","submitted_at":"2014-05-09T15:17:25Z","abstract_excerpt":"Let $G$ be a countably infinite group, and let $\\mu$ be a generating probability measure on $G$. We study the space of $\\mu$-stationary Borel probability measures on a topological $G$ space, and in particular on $Z^G$, where $Z$ is any perfect Polish space. We also study the space of $\\mu$-stationary, measurable $G$-actions on a standard, nonatomic probability space.\n  Equip the space of stationary measures with the weak* topology. When $\\mu$ has finite entropy, we show that a generic measure is an essentially free extension of the Poisson boundary of $(G,\\mu)$. When $Z$ is compact, this impli"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.2260","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"}