{"paper":{"title":"Exact Coupling of Random Walks on Polish Groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"James T. Murphy III","submitted_at":"2017-06-21T15:44:20Z","abstract_excerpt":"Exact coupling of random walks is studied. Conditions for admitting a successful exact coupling are given that are necessary and in the Abelian case also sufficient. In the Abelian case, it is shown that a random walk $S$ with step-length distribution $\\mu$ started at $0$ admits a successful exact coupling with a version $S^x$ started at $x$ if and only if there is $n\\geq 1$ with $\\mu^{n} \\wedge \\mu^{n}(x+\\cdot) \\neq 0$. Moreover, when a successful exact coupling exists, the total variation distance between $S_n$ and $S^x_n$ is determined to be $O(n^{-1/2})$ if $x$ has infinite order, or $O(\\r"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.06968","kind":"arxiv","version":4},"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"}