{"paper":{"title":"The Furstenberg Poisson Boundary and CAT(0) Cube Complexes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","math.GT"],"primary_cat":"math.GR","authors_text":"Talia Fern\\'os","submitted_at":"2015-07-20T14:34:59Z","abstract_excerpt":"We show under weak hypotheses that $\\partial X$, the Roller boundary of a finite dimensional CAT(0) cube complex $X$ is the Furstenberg-Poisson boundary of a sufficiently nice random walk on an acting group $\\Gamma$. In particular, we show that if $\\Gamma$ admits a nonelementary proper action on $X$, and $\\mu$ is a generating probability measure of finite entropy and finite first logarithmic moment, then there is a $\\mu$-stationary measure on $\\partial X$ making it the Furstenberg-Poisson boundary for the $\\mu$-random walk on $\\Gamma$. We also show that the support is contained in the closure "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.05511","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"}