{"paper":{"title":"Tight inequalities among set hitting times in Markov chains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.PR","authors_text":"Roberto Imbuzeiro Oliveira, Ross J. Kang, Simon Griffiths, Viresh Patel","submitted_at":"2012-09-01T00:42:57Z","abstract_excerpt":"Given an irreducible discrete-time Markov chain on a finite state space, we consider the largest expected hitting time $T(\\alpha)$ of a set of stationary measure at least $\\alpha$ for $\\alpha\\in(0,1)$. We obtain tight inequalities among the values of $T(\\alpha)$ for different choices of $\\alpha$. One consequence is that $T(\\alpha) \\le T(1/2)/\\alpha$ for all $\\alpha < 1/2$. As a corollary we have that, if the chain is lazy in a certain sense as well as reversible, then $T(1/2)$ is equivalent to the chain's mixing time, answering a question of Peres. We furthermore demonstrate that the inequalit"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.0039","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"}