{"paper":{"title":"On sensitivity of mixing times and cutoff","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Jonathan Hermon, Yuval Peres","submitted_at":"2016-10-14T08:05:34Z","abstract_excerpt":"A sequence of chains exhibits (total-variation) cutoff (resp., pre-cutoff) if for all $0<\\epsilon< 1/2$, the ratio $t_{\\mathrm{mix}}^{(n)}(\\epsilon)/t_{\\mathrm{mix}}^{(n)}(1-\\epsilon)$ tends to 1 as $n \\to \\infty $ (resp., the $\\limsup$ of this ratio is bounded uniformly in $\\epsilon$), where $t_{\\mathrm{mix}}^{(n)}(\\epsilon)$ is the $\\epsilon$-total-variation mixing-time of the $n$th chain in the sequence. We construct a sequence of bounded degree graphs $G_n$, such that the lazy simple random walks (LSRW) on $G_n$ satisfy the \"product condition\" $\\mathrm{gap}(G_n) t_{\\mathrm{mix}}^{(n)}(\\eps"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.04357","kind":"arxiv","version":4},"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"}