{"paper":{"title":"Exit time tails from pairwise decorrelation in hidden Markov chains, with applications to dynamical percolation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Alan Hammond, Elchanan Mossel, G\\'abor Pete","submitted_at":"2011-11-28T21:34:28Z","abstract_excerpt":"Consider a Markov process \\omega_t at equilibrium and some event C (a subset of the state-space of the process). A natural measure of correlations in the process is the pairwise correlation \\Pr[\\omega_0,\\omega_t \\in C] - \\Pr[\\omega_0 \\in C]^2. A second natural measure is the probability of the continual occurrence event \\{\\omega_s \\in C, \\forall s\\in [0,t]\\}. We show that for reversible Markov chains, and any event C, pairwise decorrelation of the event C implies a decay of the probability of the continual occurrence event \\{\\omega_s \\in C, \\forall s \\in [0,t]\\} as t\\to\\infty. We provide examp"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.6618","kind":"arxiv","version":3},"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"}