{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:KRXTQKOSDLSQP4R7CKZOAYTU7B","short_pith_number":"pith:KRXTQKOS","schema_version":"1.0","canonical_sha256":"546f3829d21ae507f23f12b2e06274f8403987bd5ec0bcd7e32960f86b35e55f","source":{"kind":"arxiv","id":"1612.05330","version":1},"attestation_state":"computed","paper":{"title":"Estimating the Spectral Gap of a Reversible Markov Chain from a Short Trajectory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR","stat.TH"],"primary_cat":"math.ST","authors_text":"David A. Levin, Yuval Peres","submitted_at":"2016-12-16T01:28:41Z","abstract_excerpt":"The spectral gap $\\gamma$ of an ergodic and reversible Markov chain is an important parameter measuring the asymptotic rate of convergence. In applications, the transition matrix $P$ may be unknown, yet one sample of the chain up to a fixed time $t$ may be observed. Hsu, Kontorovich, and Szepesvari (2015) considered the problem of estimating $\\gamma$ from this data. Let $\\pi$ be the stationary distribution of $P$, and $\\pi_\\star = \\min_x \\pi(x)$. They showed that, if $t = \\tilde{O}\\bigl(\\frac{1}{\\gamma^3 \\pi_\\star}\\bigr)$, then $\\gamma$ can be estimated to within multiplicative constants with "},"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":"1612.05330","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2016-12-16T01:28:41Z","cross_cats_sorted":["math.PR","stat.TH"],"title_canon_sha256":"08e93e1aed536023d9f62154c4b9f079f15d0d74601cc912e0a34dd64bd0cb2b","abstract_canon_sha256":"64e4d0cffac07555dd34170b76ff0dc4db12d28494f9b022f01ec38a12668126"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:54:52.052382Z","signature_b64":"ipD454MruDnLqOx7S4HqTfXkw3HiHy2wsvq5cb0FFVEZ2uCXzHHVoOIEUXeEHnbVrvRRVSASeG/r+hGWOSNHAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"546f3829d21ae507f23f12b2e06274f8403987bd5ec0bcd7e32960f86b35e55f","last_reissued_at":"2026-05-18T00:54:52.051963Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:54:52.051963Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Estimating the Spectral Gap of a Reversible Markov Chain from a Short Trajectory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR","stat.TH"],"primary_cat":"math.ST","authors_text":"David A. Levin, Yuval Peres","submitted_at":"2016-12-16T01:28:41Z","abstract_excerpt":"The spectral gap $\\gamma$ of an ergodic and reversible Markov chain is an important parameter measuring the asymptotic rate of convergence. In applications, the transition matrix $P$ may be unknown, yet one sample of the chain up to a fixed time $t$ may be observed. Hsu, Kontorovich, and Szepesvari (2015) considered the problem of estimating $\\gamma$ from this data. Let $\\pi$ be the stationary distribution of $P$, and $\\pi_\\star = \\min_x \\pi(x)$. They showed that, if $t = \\tilde{O}\\bigl(\\frac{1}{\\gamma^3 \\pi_\\star}\\bigr)$, then $\\gamma$ can be estimated to within multiplicative constants with "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.05330","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":"1612.05330","created_at":"2026-05-18T00:54:52.052019+00:00"},{"alias_kind":"arxiv_version","alias_value":"1612.05330v1","created_at":"2026-05-18T00:54:52.052019+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.05330","created_at":"2026-05-18T00:54:52.052019+00:00"},{"alias_kind":"pith_short_12","alias_value":"KRXTQKOSDLSQ","created_at":"2026-05-18T12:30:29.479603+00:00"},{"alias_kind":"pith_short_16","alias_value":"KRXTQKOSDLSQP4R7","created_at":"2026-05-18T12:30:29.479603+00:00"},{"alias_kind":"pith_short_8","alias_value":"KRXTQKOS","created_at":"2026-05-18T12:30:29.479603+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/KRXTQKOSDLSQP4R7CKZOAYTU7B","json":"https://pith.science/pith/KRXTQKOSDLSQP4R7CKZOAYTU7B.json","graph_json":"https://pith.science/api/pith-number/KRXTQKOSDLSQP4R7CKZOAYTU7B/graph.json","events_json":"https://pith.science/api/pith-number/KRXTQKOSDLSQP4R7CKZOAYTU7B/events.json","paper":"https://pith.science/paper/KRXTQKOS"},"agent_actions":{"view_html":"https://pith.science/pith/KRXTQKOSDLSQP4R7CKZOAYTU7B","download_json":"https://pith.science/pith/KRXTQKOSDLSQP4R7CKZOAYTU7B.json","view_paper":"https://pith.science/paper/KRXTQKOS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1612.05330&json=true","fetch_graph":"https://pith.science/api/pith-number/KRXTQKOSDLSQP4R7CKZOAYTU7B/graph.json","fetch_events":"https://pith.science/api/pith-number/KRXTQKOSDLSQP4R7CKZOAYTU7B/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KRXTQKOSDLSQP4R7CKZOAYTU7B/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KRXTQKOSDLSQP4R7CKZOAYTU7B/action/storage_attestation","attest_author":"https://pith.science/pith/KRXTQKOSDLSQP4R7CKZOAYTU7B/action/author_attestation","sign_citation":"https://pith.science/pith/KRXTQKOSDLSQP4R7CKZOAYTU7B/action/citation_signature","submit_replication":"https://pith.science/pith/KRXTQKOSDLSQP4R7CKZOAYTU7B/action/replication_record"}},"created_at":"2026-05-18T00:54:52.052019+00:00","updated_at":"2026-05-18T00:54:52.052019+00:00"}