{"paper":{"title":"Random Walks on countable groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR","math.PR"],"primary_cat":"math.DS","authors_text":"Michael Bj\\\"orklund","submitted_at":"2015-02-13T16:02:44Z","abstract_excerpt":"We begin by giving a new proof of the equivalence between the Liouville property and vanishing of the drift for symmetric random walks with finite first moments on finitely generated groups; a result which was first established by Kaimanovich-Vershik and Karlsson-Ledrappier. We then proceed to prove that the product of the Poisson boundary of any countable measured group $(G,\\mu)$ with any ergodic $(G,\\check{\\mu})$-space is still ergodic, which in particular yields a new proof of weak mixing for the double Poisson boundary of $(G,\\mu)$ when $\\mu$ is symmetric. Finally, we characterize the fail"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.04038","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"}