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Suitably modified results hold in discrete time and/or without the reversibility assumption. The key technical tool is a construction of a random set A such that the hitting time of A is both light-tailed and a stationary time for the chain. We note that essentially the same results were obtained independently by Peres and Sousi [arXiv:1108.0133]."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1108.1708","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-08-08T13:50:42Z","cross_cats_sorted":[],"title_canon_sha256":"320bea8ff9b20aafef1e28bab4d44b35e7aa306d4dfee072f72045f751360c2f","abstract_canon_sha256":"6c45889d9e4212103c3cac83d7290f0032f9dd897d6d0092f4fb78b8a1a0945c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:47:01.408091Z","signature_b64":"N/+bRyAGGjXj/wxrxzVGMUMFlHzTbbFuZ5NJLQuwVsAlKFIF3VQHhLKrbVDO6UnQLmLPsv5U9jaVr0QgSV/rBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b97bfc34773165dd39e3fb5a8257230278f3291d5ef11af7e90f613fea5082cb","last_reissued_at":"2026-05-18T03:47:01.407567Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:47:01.407567Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Mixing and hitting times for finite Markov chains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Roberto Imbuzeiro Oliveira","submitted_at":"2011-08-08T13:50:42Z","abstract_excerpt":"Let 0<\\alpha<1/2. 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