{"paper":{"title":"Mixing time estimation in reversible Markov chains from a single sample path","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","math.PR","stat.ML","stat.TH"],"primary_cat":"math.ST","authors_text":"Aryeh Kontorovich, Csaba Szepesv\\'ari, Daniel Hsu, David A. Levin, Yuval Peres","submitted_at":"2017-08-24T12:05:11Z","abstract_excerpt":"The spectral gap $\\gamma$ of a finite, ergodic, and reversible Markov chain is an important parameter measuring the asymptotic rate of convergence. In applications, the transition matrix $P$ may be unknown, yet one sample of the chain up to a fixed time $n$ may be observed. We consider here the problem of estimating $\\gamma$ from this data. Let $\\pi$ be the stationary distribution of $P$, and $\\pi_\\star = \\min_x \\pi(x)$. We show that if $n = \\tilde{O}\\bigl(\\frac{1}{\\gamma \\pi_\\star}\\bigr)$, then $\\gamma$ can be estimated to within multiplicative constants with high probability. When $\\pi$ is u"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.07367","kind":"arxiv","version":1},"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"}