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The equilibrium distribution is uniform over the set of all $n$-PM.\n  We establish cutoff for the $k$-PM RW whenever $2 \\le k \\ll n$. If $k \\gg 1$, then the mixing time is $\\tfrac nk \\log n$ to leading order. The case $k = 2$ was established by Diaconis and Holmes (2002) by relating the $2$-PM RW to "},"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":"2108.11890","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2021-08-26T16:27:33Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"36aaa6d88ccb6a0dde94381331a94809a38390bfebd7e011c882968f23b451ef","abstract_canon_sha256":"f0e6adb70c7c65b8e56713ef072c4880ca858a7190a280663621f0ec56631c76"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:20:48.593099Z","signature_b64":"zYJ0ZXlFHyRYbUKXEs4805f2hBmlTEoClBAnBDrNvSTXJ2HukDNDuH8tQObU/zrlxTZG2XUcU0FiWO2g4Wy6DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4078e5c9d41d9bc7abbdfdb637a267893c8820e788f1e12b235ba4a9616113fc","last_reissued_at":"2026-07-05T08:20:48.592567Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:20:48.592567Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Cutoff for Rewiring Dynamics on Perfect Matchings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.PR","authors_text":"Sam Olesker-Taylor","submitted_at":"2021-08-26T16:27:33Z","abstract_excerpt":"We establish cutoff for a natural random walk (RW) on the set of perfect matchings (PMs). An $n$-PM is a pairing of $2n$ objects. The $k$-PM RW selects $k$ pairs uniformly at random, disassociates the corresponding $2k$ objects, then chooses a new pairing on these $2k$ objects uniformly at random. The equilibrium distribution is uniform over the set of all $n$-PM.\n  We establish cutoff for the $k$-PM RW whenever $2 \\le k \\ll n$. If $k \\gg 1$, then the mixing time is $\\tfrac nk \\log n$ to leading order. 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