{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:3MIIQIJF3ZO4JETIYLCVBPP2CZ","short_pith_number":"pith:3MIIQIJF","schema_version":"1.0","canonical_sha256":"db10882125de5dc49268c2c550bdfa1654ae371d58be6214aa71591214c5aecd","source":{"kind":"arxiv","id":"1111.0151","version":1},"attestation_state":"computed","paper":{"title":"The Distribution of Mixing Times in Markov Chains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Jeffrey J. Hunter","submitted_at":"2011-11-01T09:25:14Z","abstract_excerpt":"The distribution of the \"mixing time\" or the \"time to stationarity\" in a discrete time irreducible Markov chain, starting in state i, can be defined as the number of trials to reach a state sampled from the stationary distribution of the Markov chain. Expressions for the probability generating function, and hence the probability distribution of the mixing time starting in state i are derived and special cases explored. This extends the results of the author regarding the expected time to mixing [J.J. Hunter, Mixing times with applications to perturbed Markov chains, Linear Algebra Appl. 417 (2"},"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":"1111.0151","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-11-01T09:25:14Z","cross_cats_sorted":[],"title_canon_sha256":"4e1e31b80203254332c1884cd88cbeb32ae6d59af87548014c2dcce6bdaa9ac6","abstract_canon_sha256":"12b9a8897ffd7d5837a50202d26c1842d39d849b8328fd87945e8d34da2f5e4d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:57:24.409806Z","signature_b64":"ErjfwittLsoNzjAKHIPmLckYqB8nypqmTTBlnNhnI4SCH59DllLSr/PpU7DnGjqFSoSyt+cKrkpMHbsNaQGZDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"db10882125de5dc49268c2c550bdfa1654ae371d58be6214aa71591214c5aecd","last_reissued_at":"2026-05-18T02:57:24.409105Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:57:24.409105Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Distribution of Mixing Times in Markov Chains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Jeffrey J. Hunter","submitted_at":"2011-11-01T09:25:14Z","abstract_excerpt":"The distribution of the \"mixing time\" or the \"time to stationarity\" in a discrete time irreducible Markov chain, starting in state i, can be defined as the number of trials to reach a state sampled from the stationary distribution of the Markov chain. Expressions for the probability generating function, and hence the probability distribution of the mixing time starting in state i are derived and special cases explored. This extends the results of the author regarding the expected time to mixing [J.J. Hunter, Mixing times with applications to perturbed Markov chains, Linear Algebra Appl. 417 (2"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.0151","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1111.0151","created_at":"2026-05-18T02:57:24.409215+00:00"},{"alias_kind":"arxiv_version","alias_value":"1111.0151v1","created_at":"2026-05-18T02:57:24.409215+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.0151","created_at":"2026-05-18T02:57:24.409215+00:00"},{"alias_kind":"pith_short_12","alias_value":"3MIIQIJF3ZO4","created_at":"2026-05-18T12:26:18.847500+00:00"},{"alias_kind":"pith_short_16","alias_value":"3MIIQIJF3ZO4JETI","created_at":"2026-05-18T12:26:18.847500+00:00"},{"alias_kind":"pith_short_8","alias_value":"3MIIQIJF","created_at":"2026-05-18T12:26:18.847500+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/3MIIQIJF3ZO4JETIYLCVBPP2CZ","json":"https://pith.science/pith/3MIIQIJF3ZO4JETIYLCVBPP2CZ.json","graph_json":"https://pith.science/api/pith-number/3MIIQIJF3ZO4JETIYLCVBPP2CZ/graph.json","events_json":"https://pith.science/api/pith-number/3MIIQIJF3ZO4JETIYLCVBPP2CZ/events.json","paper":"https://pith.science/paper/3MIIQIJF"},"agent_actions":{"view_html":"https://pith.science/pith/3MIIQIJF3ZO4JETIYLCVBPP2CZ","download_json":"https://pith.science/pith/3MIIQIJF3ZO4JETIYLCVBPP2CZ.json","view_paper":"https://pith.science/paper/3MIIQIJF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1111.0151&json=true","fetch_graph":"https://pith.science/api/pith-number/3MIIQIJF3ZO4JETIYLCVBPP2CZ/graph.json","fetch_events":"https://pith.science/api/pith-number/3MIIQIJF3ZO4JETIYLCVBPP2CZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3MIIQIJF3ZO4JETIYLCVBPP2CZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3MIIQIJF3ZO4JETIYLCVBPP2CZ/action/storage_attestation","attest_author":"https://pith.science/pith/3MIIQIJF3ZO4JETIYLCVBPP2CZ/action/author_attestation","sign_citation":"https://pith.science/pith/3MIIQIJF3ZO4JETIYLCVBPP2CZ/action/citation_signature","submit_replication":"https://pith.science/pith/3MIIQIJF3ZO4JETIYLCVBPP2CZ/action/replication_record"}},"created_at":"2026-05-18T02:57:24.409215+00:00","updated_at":"2026-05-18T02:57:24.409215+00:00"}