{"paper":{"title":"Cutoff for product replacement on finite groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Alex Zhai, Ryokichi Tanaka, Yuval Peres","submitted_at":"2018-05-14T06:51:21Z","abstract_excerpt":"We analyze a Markov chain, known as the product replacement chain, on the set of generating $n$-tuples of a fixed finite group $G$. We show that as $n \\rightarrow \\infty$, the total-variation mixing time of the chain has a cutoff at time $\\frac{3}{2} n \\log n$ with window of order $n$. This generalizes a result of Ben-Hamou and Peres (who established the result for $G = \\mathbb{Z}/2$) and confirms a conjecture of Diaconis and Saloff-Coste that for an arbitrary but fixed finite group, the mixing time of the product replacement chain is $O(n \\log n)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.05025","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"}