{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:TJE62HHEVT2WZEDCEVOBKGU7YA","short_pith_number":"pith:TJE62HHE","schema_version":"1.0","canonical_sha256":"9a49ed1ce4acf56c9062255c151a9fc00ebb92a0795d5ab3a44ec6a446320159","source":{"kind":"arxiv","id":"1408.0822","version":1},"attestation_state":"computed","paper":{"title":"Surprise probabilities in Markov chains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Alex Zhai, James Norris, Yuval Peres","submitted_at":"2014-08-04T21:39:01Z","abstract_excerpt":"In a Markov chain started at a state $x$, the hitting time $\\tau(y)$ is the first time that the chain reaches another state $y$. We study the probability $\\mathbf{P}_x(\\tau(y) = t)$ that the first visit to $y$ occurs precisely at a given time $t$. Informally speaking, the event that a new state is visited at a large time $t$ may be considered a \"surprise\". We prove the following three bounds:\n  1) In any Markov chain with $n$ states, $\\mathbf{P}_x(\\tau(y) = t) \\le \\frac{n}{t}$.\n  2) In a reversible chain with $n$ states, $\\mathbf{P}_x(\\tau(y) = t) \\le \\frac{\\sqrt{2n}}{t}$ for $t \\ge 4n + 4$.\n "},"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":"1408.0822","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-08-04T21:39:01Z","cross_cats_sorted":[],"title_canon_sha256":"d3f3c3fc1ba1bf9c04beaac71b8d02c9284a6c1274aef40b4aa922a97bd2f573","abstract_canon_sha256":"a64ccd66ffbecb2c709fb61da5b0b4bb8af3088c6226c21fdf7181972b46d298"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:45:50.315457Z","signature_b64":"3xz+eXg36811J1Rks2fntdW+r5qX/6hOIrmjsw65i7DHl+RB9g9md5gSkIKfZL6LGVcQtvC3L8ykwdXQlsTmDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9a49ed1ce4acf56c9062255c151a9fc00ebb92a0795d5ab3a44ec6a446320159","last_reissued_at":"2026-05-18T02:45:50.314868Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:45:50.314868Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Surprise probabilities in Markov chains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Alex Zhai, James Norris, Yuval Peres","submitted_at":"2014-08-04T21:39:01Z","abstract_excerpt":"In a Markov chain started at a state $x$, the hitting time $\\tau(y)$ is the first time that the chain reaches another state $y$. We study the probability $\\mathbf{P}_x(\\tau(y) = t)$ that the first visit to $y$ occurs precisely at a given time $t$. Informally speaking, the event that a new state is visited at a large time $t$ may be considered a \"surprise\". We prove the following three bounds:\n  1) In any Markov chain with $n$ states, $\\mathbf{P}_x(\\tau(y) = t) \\le \\frac{n}{t}$.\n  2) In a reversible chain with $n$ states, $\\mathbf{P}_x(\\tau(y) = t) \\le \\frac{\\sqrt{2n}}{t}$ for $t \\ge 4n + 4$.\n "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.0822","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":"1408.0822","created_at":"2026-05-18T02:45:50.314945+00:00"},{"alias_kind":"arxiv_version","alias_value":"1408.0822v1","created_at":"2026-05-18T02:45:50.314945+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.0822","created_at":"2026-05-18T02:45:50.314945+00:00"},{"alias_kind":"pith_short_12","alias_value":"TJE62HHEVT2W","created_at":"2026-05-18T12:28:49.207871+00:00"},{"alias_kind":"pith_short_16","alias_value":"TJE62HHEVT2WZEDC","created_at":"2026-05-18T12:28:49.207871+00:00"},{"alias_kind":"pith_short_8","alias_value":"TJE62HHE","created_at":"2026-05-18T12:28:49.207871+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/TJE62HHEVT2WZEDCEVOBKGU7YA","json":"https://pith.science/pith/TJE62HHEVT2WZEDCEVOBKGU7YA.json","graph_json":"https://pith.science/api/pith-number/TJE62HHEVT2WZEDCEVOBKGU7YA/graph.json","events_json":"https://pith.science/api/pith-number/TJE62HHEVT2WZEDCEVOBKGU7YA/events.json","paper":"https://pith.science/paper/TJE62HHE"},"agent_actions":{"view_html":"https://pith.science/pith/TJE62HHEVT2WZEDCEVOBKGU7YA","download_json":"https://pith.science/pith/TJE62HHEVT2WZEDCEVOBKGU7YA.json","view_paper":"https://pith.science/paper/TJE62HHE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1408.0822&json=true","fetch_graph":"https://pith.science/api/pith-number/TJE62HHEVT2WZEDCEVOBKGU7YA/graph.json","fetch_events":"https://pith.science/api/pith-number/TJE62HHEVT2WZEDCEVOBKGU7YA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TJE62HHEVT2WZEDCEVOBKGU7YA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TJE62HHEVT2WZEDCEVOBKGU7YA/action/storage_attestation","attest_author":"https://pith.science/pith/TJE62HHEVT2WZEDCEVOBKGU7YA/action/author_attestation","sign_citation":"https://pith.science/pith/TJE62HHEVT2WZEDCEVOBKGU7YA/action/citation_signature","submit_replication":"https://pith.science/pith/TJE62HHEVT2WZEDCEVOBKGU7YA/action/replication_record"}},"created_at":"2026-05-18T02:45:50.314945+00:00","updated_at":"2026-05-18T02:45:50.314945+00:00"}