{"paper":{"title":"A Lower Bound for the Mixing Time of the Random-to-Random Insertions Shuffle","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Eliran Subag","submitted_at":"2011-12-26T11:49:34Z","abstract_excerpt":"The best known lower and upper bounds on the mixing time for the random-to-random insertions shuffle are $(1/2-o(1))n\\log n$ and $(2+o(1))n\\log n$. A long standing open problem is to prove that the mixing time exhibits a cutoff. In particular, Diaconis conjectured that the cutoff occurs at $3/4n\\log n$. Our main result is a lower bound of $t_n = (3/4-o(1))n\\log n$, corresponding to this conjecture.\n  Our method is based on analysis of the positions of cards yet-to-be-removed. We show that for large $n$ and $t_n$ as above, there exists $f(n)=\\Theta(\\sqrt{n\\log n})$ such that, with high probabil"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.5847","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"}