{"paper":{"title":"Cutoff for Random Walks on Upper Triangular Matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.PR","authors_text":"Jonathan Hermon, Sam Olesker-Taylor","submitted_at":"2019-11-07T17:22:00Z","abstract_excerpt":"Consider the random Cayley graph of a finite group $G$ with respect to $k$ generators chosen uniformly at random, with $1 \\ll \\log k \\ll \\log |G|$ (ie $1 \\ll k = |G|^{o(1)}$). A conjecture of Aldous and Diaconis (1985) asserts, for $k\\gg\\log|G|$, that the random walk on this graph exhibits cutoff.\n  When $\\log k \\lesssim \\log\\log|G|$ (ie $k = (\\log |G|)^{\\mathcal O(1)}$), the only example of a non-Abelian group for which cutoff has been established is the dihedral group. We establish cutoff (as $p\\to infty$) for the group of $d \\times d$ unit upper triangular matrices with integer entries modu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1911.02974","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1911.02974/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}