{"paper":{"title":"A technical report on hitting times, mixing and cutoff","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Jonathan Hermon","submitted_at":"2015-01-08T14:35:31Z","abstract_excerpt":"Consider a sequence of continuous-time irreducible reversible Markov chains and a sequence of initial distributions, $\\mu_n$. The sequence is said to exhibit $\\mu_n$-cutoff if the convergence to stationarity in total variation distance is abrupt, w.r.t. this sequence of initial distributions.\n  In this work we give a characterization of $\\mu_n$-cutoff for an arbitrary sequence of initial distributions $\\mu_n$ (in the above setup). Our characterization is expressed in terms of hitting times of sets which are \"worst\" w.r.t. $\\mu_n$.\n  Consider a Markov chain on $\\Omega$ whose stationary distribu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.01869","kind":"arxiv","version":6},"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"}