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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1112.5847","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-12-26T11:49:34Z","cross_cats_sorted":[],"title_canon_sha256":"525730308710d2010e063c9517e0d3a5d7a5aeb460a293c57b9b8997ca6545ea","abstract_canon_sha256":"bfccc50d69c2f0a13210bfd9277c82931819c0543f3588c994ba56c2a70132b7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:21:26.937742Z","signature_b64":"+zcVjtx202kUKcZGEGU4zXo/wFRfJ+WifXyTZKzMR20DsL0tFD2609zra1nkJ9xRDBLTPDbOh6SRIFxCDkb5BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ce8fc2abf98dac1c29474b27ca2b9550a9ec9eb3f61e2ba20cdb9c091d83fc2e","last_reissued_at":"2026-05-18T02:21:26.937021Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:21:26.937021Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1112.5847","created_at":"2026-05-18T02:21:26.937162+00:00"},{"alias_kind":"arxiv_version","alias_value":"1112.5847v2","created_at":"2026-05-18T02:21:26.937162+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.5847","created_at":"2026-05-18T02:21:26.937162+00:00"},{"alias_kind":"pith_short_12","alias_value":"Z2H4FK7ZRWWB","created_at":"2026-05-18T12:26:47.523578+00:00"},{"alias_kind":"pith_short_16","alias_value":"Z2H4FK7ZRWWBYKKH","created_at":"2026-05-18T12:26:47.523578+00:00"},{"alias_kind":"pith_short_8","alias_value":"Z2H4FK7Z","created_at":"2026-05-18T12:26:47.523578+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/Z2H4FK7ZRWWBYKKHJMT4UK4VKC","json":"https://pith.science/pith/Z2H4FK7ZRWWBYKKHJMT4UK4VKC.json","graph_json":"https://pith.science/api/pith-number/Z2H4FK7ZRWWBYKKHJMT4UK4VKC/graph.json","events_json":"https://pith.science/api/pith-number/Z2H4FK7ZRWWBYKKHJMT4UK4VKC/events.json","paper":"https://pith.science/paper/Z2H4FK7Z"},"agent_actions":{"view_html":"https://pith.science/pith/Z2H4FK7ZRWWBYKKHJMT4UK4VKC","download_json":"https://pith.science/pith/Z2H4FK7ZRWWBYKKHJMT4UK4VKC.json","view_paper":"https://pith.science/paper/Z2H4FK7Z","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1112.5847&json=true","fetch_graph":"https://pith.science/api/pith-number/Z2H4FK7ZRWWBYKKHJMT4UK4VKC/graph.json","fetch_events":"https://pith.science/api/pith-number/Z2H4FK7ZRWWBYKKHJMT4UK4VKC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/Z2H4FK7ZRWWBYKKHJMT4UK4VKC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/Z2H4FK7ZRWWBYKKHJMT4UK4VKC/action/storage_attestation","attest_author":"https://pith.science/pith/Z2H4FK7ZRWWBYKKHJMT4UK4VKC/action/author_attestation","sign_citation":"https://pith.science/pith/Z2H4FK7ZRWWBYKKHJMT4UK4VKC/action/citation_signature","submit_replication":"https://pith.science/pith/Z2H4FK7ZRWWBYKKHJMT4UK4VKC/action/replication_record"}},"created_at":"2026-05-18T02:21:26.937162+00:00","updated_at":"2026-05-18T02:21:26.937162+00:00"}