{"paper":{"title":"Thompson's group $F$ is not Liouville","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.GR","authors_text":"Vadim A. Kaimanovich","submitted_at":"2016-02-09T13:14:00Z","abstract_excerpt":"We prove that random walks on Thompson's group $F$ driven by strictly non-degenerate finitely supported probability measures $\\mu$ have a non-trivial Poisson boundary. The proof consists in an explicit construction of two different non-trivial $\\mu$-boundaries. Both of them are defined in terms of the Schreier graph $\\Gamma$ on the dyadic-rational orbit of the canonical action of $F$ on the unit interval (actually, we consider a natural embedding of $F$ into the group $PLF({\\mathbb R})$ of piecewise linear homeomorphisms of the real line, and realize $\\Gamma$ on the dyadic-rational orbit in ${"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.02971","kind":"arxiv","version":3},"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"}