{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:XF57YNDXGFS52OPD7NNIEVZDAJ","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"6c45889d9e4212103c3cac83d7290f0032f9dd897d6d0092f4fb78b8a1a0945c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-08-08T13:50:42Z","title_canon_sha256":"320bea8ff9b20aafef1e28bab4d44b35e7aa306d4dfee072f72045f751360c2f"},"schema_version":"1.0","source":{"id":"1108.1708","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1108.1708","created_at":"2026-05-18T03:47:01Z"},{"alias_kind":"arxiv_version","alias_value":"1108.1708v2","created_at":"2026-05-18T03:47:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.1708","created_at":"2026-05-18T03:47:01Z"},{"alias_kind":"pith_short_12","alias_value":"XF57YNDXGFS5","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_16","alias_value":"XF57YNDXGFS52OPD","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_8","alias_value":"XF57YNDX","created_at":"2026-05-18T12:26:44Z"}],"graph_snapshots":[{"event_id":"sha256:da591c7b236fc923c5c2a7d24f6f4b81156a425d20ff16bb7af19f7601b797f2","target":"graph","created_at":"2026-05-18T03:47:01Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"Let 0<\\alpha<1/2. We show that the mixing time of a continuous-time reversible Markov chain on a finite state space is about as large as the largest expected hitting time of a subset of stationary measure at least \\alpha of the state space. 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].","authors_text":"Roberto Imbuzeiro Oliveira","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-08-08T13:50:42Z","title":"Mixing and hitting times for finite Markov chains"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.1708","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:74c3f5c19a3e4602a323da3ddfc59c0088cc83e761fc0fe4a5c7042538c9c803","target":"record","created_at":"2026-05-18T03:47:01Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"6c45889d9e4212103c3cac83d7290f0032f9dd897d6d0092f4fb78b8a1a0945c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-08-08T13:50:42Z","title_canon_sha256":"320bea8ff9b20aafef1e28bab4d44b35e7aa306d4dfee072f72045f751360c2f"},"schema_version":"1.0","source":{"id":"1108.1708","kind":"arxiv","version":2}},"canonical_sha256":"b97bfc34773165dd39e3fb5a8257230278f3291d5ef11af7e90f613fea5082cb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b97bfc34773165dd39e3fb5a8257230278f3291d5ef11af7e90f613fea5082cb","first_computed_at":"2026-05-18T03:47:01.407567Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:47:01.407567Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"N/+bRyAGGjXj/wxrxzVGMUMFlHzTbbFuZ5NJLQuwVsAlKFIF3VQHhLKrbVDO6UnQLmLPsv5U9jaVr0QgSV/rBg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:47:01.408091Z","signed_message":"canonical_sha256_bytes"},"source_id":"1108.1708","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:74c3f5c19a3e4602a323da3ddfc59c0088cc83e761fc0fe4a5c7042538c9c803","sha256:da591c7b236fc923c5c2a7d24f6f4b81156a425d20ff16bb7af19f7601b797f2"],"state_sha256":"2ccbcc2428ea5c1c18f4d7f83e1312a71b851935ee4a65dbce875c8e7afabb63"}