{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:VML7EY3JJABSEFK4CPRKP6WH6S","short_pith_number":"pith:VML7EY3J","schema_version":"1.0","canonical_sha256":"ab17f26369480322155c13e2a7fac7f4abcd6dc2c7a3218cea65995dc521fc6a","source":{"kind":"arxiv","id":"1410.4716","version":1},"attestation_state":"computed","paper":{"title":"Approximating Laplace transforms of meeting times for some symmetric Markov chains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Yu-Ting Chen","submitted_at":"2014-10-17T13:16:17Z","abstract_excerpt":"We study distributions of meeting times for finite symmetric Markov chains. For Markov kernels defined on large state spaces which satisfy certain weak inhomogeneity in return probabilities of points up to large numbers of steps, we obtain approximation, with explicit error bounds, of the Laplace transforms of some meeting times (without scaling) by ratios of Green functions closely related to hitting times of points. In studying this approximation, we identify some key matrix power series in Markov kernels weighted with solutions to a discrete transport-like equation with explicit coefficient"},"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":"1410.4716","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-10-17T13:16:17Z","cross_cats_sorted":[],"title_canon_sha256":"d7a6aa2f1e431689514f93041b241bc1390e3a709432e535b7ff1b773ec5d29c","abstract_canon_sha256":"ea335705e1afcea826c2638578a0044bf3aca7c688417a40d74ecba9f99b2476"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:39:54.856520Z","signature_b64":"MDuiAIBKcMB86Do1DBUcEcuvUkA0QBrbO4EgszOedlkNIq4ETanL7xGSxYdFC81nKilADq5IPw1gvLYYevPcAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ab17f26369480322155c13e2a7fac7f4abcd6dc2c7a3218cea65995dc521fc6a","last_reissued_at":"2026-05-18T02:39:54.856009Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:39:54.856009Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Approximating Laplace transforms of meeting times for some symmetric Markov chains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Yu-Ting Chen","submitted_at":"2014-10-17T13:16:17Z","abstract_excerpt":"We study distributions of meeting times for finite symmetric Markov chains. For Markov kernels defined on large state spaces which satisfy certain weak inhomogeneity in return probabilities of points up to large numbers of steps, we obtain approximation, with explicit error bounds, of the Laplace transforms of some meeting times (without scaling) by ratios of Green functions closely related to hitting times of points. In studying this approximation, we identify some key matrix power series in Markov kernels weighted with solutions to a discrete transport-like equation with explicit coefficient"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.4716","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":"1410.4716","created_at":"2026-05-18T02:39:54.856082+00:00"},{"alias_kind":"arxiv_version","alias_value":"1410.4716v1","created_at":"2026-05-18T02:39:54.856082+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.4716","created_at":"2026-05-18T02:39:54.856082+00:00"},{"alias_kind":"pith_short_12","alias_value":"VML7EY3JJABS","created_at":"2026-05-18T12:28:54.890064+00:00"},{"alias_kind":"pith_short_16","alias_value":"VML7EY3JJABSEFK4","created_at":"2026-05-18T12:28:54.890064+00:00"},{"alias_kind":"pith_short_8","alias_value":"VML7EY3J","created_at":"2026-05-18T12:28:54.890064+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/VML7EY3JJABSEFK4CPRKP6WH6S","json":"https://pith.science/pith/VML7EY3JJABSEFK4CPRKP6WH6S.json","graph_json":"https://pith.science/api/pith-number/VML7EY3JJABSEFK4CPRKP6WH6S/graph.json","events_json":"https://pith.science/api/pith-number/VML7EY3JJABSEFK4CPRKP6WH6S/events.json","paper":"https://pith.science/paper/VML7EY3J"},"agent_actions":{"view_html":"https://pith.science/pith/VML7EY3JJABSEFK4CPRKP6WH6S","download_json":"https://pith.science/pith/VML7EY3JJABSEFK4CPRKP6WH6S.json","view_paper":"https://pith.science/paper/VML7EY3J","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1410.4716&json=true","fetch_graph":"https://pith.science/api/pith-number/VML7EY3JJABSEFK4CPRKP6WH6S/graph.json","fetch_events":"https://pith.science/api/pith-number/VML7EY3JJABSEFK4CPRKP6WH6S/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VML7EY3JJABSEFK4CPRKP6WH6S/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VML7EY3JJABSEFK4CPRKP6WH6S/action/storage_attestation","attest_author":"https://pith.science/pith/VML7EY3JJABSEFK4CPRKP6WH6S/action/author_attestation","sign_citation":"https://pith.science/pith/VML7EY3JJABSEFK4CPRKP6WH6S/action/citation_signature","submit_replication":"https://pith.science/pith/VML7EY3JJABSEFK4CPRKP6WH6S/action/replication_record"}},"created_at":"2026-05-18T02:39:54.856082+00:00","updated_at":"2026-05-18T02:39:54.856082+00:00"}