{"paper":{"title":"Boundaries of $\\mathbb{Z}^n$-free groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Andrei Malyutin, Denis Serbin, Tatiana Nagnibeda","submitted_at":"2012-11-14T07:34:51Z","abstract_excerpt":"In this paper we study random walks on a finitely generated group $G$ which has a free action on a $\\mathbb{Z}^n$-tree. We show that if $G$ is non-abelian and acts minimally, freely and without inversions on a locally finite $\\mathbb{Z}^n$-tree $\\Gamma$ with the set of open ends ${\\rm Ends}(\\Gamma)$, then for every non-degenerate probability measure $\\mu$ on $G$ there exists a unique $\\mu$-stationary probability measure $\\nu_\\mu$ on ${\\rm Ends}(\\Gamma)$, and the space $({\\rm Ends}(\\Gamma), \\nu_\\mu)$ is a $\\mu$-boundary. Moreover, if $\\mu$ has finite first moment with respect to the word metric"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.3226","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"}