{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:Q2YCSMQ7AXOZSCBLSGN5XHH6XA","short_pith_number":"pith:Q2YCSMQ7","schema_version":"1.0","canonical_sha256":"86b029321f05dd99082b919bdb9cfeb823326045528415fc1c3ce4ba19cf4bd8","source":{"kind":"arxiv","id":"1109.5684","version":3},"attestation_state":"computed","paper":{"title":"Mean field conditions for coalescing random walks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Roberto Imbuzeiro Oliveira","submitted_at":"2011-09-26T19:45:31Z","abstract_excerpt":"The main results in this paper are about the full coalescence time $\\mathsf{C}$ of a system of coalescing random walks over a finite graph $G$. Letting $\\mathsf{m}(G)$ denote the mean meeting time of two such walkers, we give sufficient conditions under which $\\mathbf{E}[\\mathsf{C}]\\approx 2\\mathsf{m}(G)$ and $\\mathsf{C}/\\mathsf{m}(G)$ has approximately the same law as in the \"mean field\" setting of a large complete graph. One of our theorems is that mean field behavior occurs over all vertex-transitive graphs whose mixing times are much smaller than $\\mathsf{m}(G)$; this nearly solves an open"},"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":"1109.5684","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-09-26T19:45:31Z","cross_cats_sorted":[],"title_canon_sha256":"45ab1899db7dcddde7304c576c52478faba6ea15beadea632cd9971bef918aff","abstract_canon_sha256":"44abe05eb916dc4dbfd45a1947861d1db68f77f38e0549b26610f810c094030a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:11:33.728876Z","signature_b64":"i3aApSfloCi3QOmDs/CtYWGEM+jFpW/S+hmep71SdcoPuR1IjVAswmM4KuC1bgyaZzDwopTzVzDa10Rzb6CqDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"86b029321f05dd99082b919bdb9cfeb823326045528415fc1c3ce4ba19cf4bd8","last_reissued_at":"2026-05-18T03:11:33.728208Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:11:33.728208Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Mean field conditions for coalescing random walks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Roberto Imbuzeiro Oliveira","submitted_at":"2011-09-26T19:45:31Z","abstract_excerpt":"The main results in this paper are about the full coalescence time $\\mathsf{C}$ of a system of coalescing random walks over a finite graph $G$. Letting $\\mathsf{m}(G)$ denote the mean meeting time of two such walkers, we give sufficient conditions under which $\\mathbf{E}[\\mathsf{C}]\\approx 2\\mathsf{m}(G)$ and $\\mathsf{C}/\\mathsf{m}(G)$ has approximately the same law as in the \"mean field\" setting of a large complete graph. One of our theorems is that mean field behavior occurs over all vertex-transitive graphs whose mixing times are much smaller than $\\mathsf{m}(G)$; this nearly solves an open"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.5684","kind":"arxiv","version":3},"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":"1109.5684","created_at":"2026-05-18T03:11:33.728331+00:00"},{"alias_kind":"arxiv_version","alias_value":"1109.5684v3","created_at":"2026-05-18T03:11:33.728331+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.5684","created_at":"2026-05-18T03:11:33.728331+00:00"},{"alias_kind":"pith_short_12","alias_value":"Q2YCSMQ7AXOZ","created_at":"2026-05-18T12:26:39.201973+00:00"},{"alias_kind":"pith_short_16","alias_value":"Q2YCSMQ7AXOZSCBL","created_at":"2026-05-18T12:26:39.201973+00:00"},{"alias_kind":"pith_short_8","alias_value":"Q2YCSMQ7","created_at":"2026-05-18T12:26:39.201973+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/Q2YCSMQ7AXOZSCBLSGN5XHH6XA","json":"https://pith.science/pith/Q2YCSMQ7AXOZSCBLSGN5XHH6XA.json","graph_json":"https://pith.science/api/pith-number/Q2YCSMQ7AXOZSCBLSGN5XHH6XA/graph.json","events_json":"https://pith.science/api/pith-number/Q2YCSMQ7AXOZSCBLSGN5XHH6XA/events.json","paper":"https://pith.science/paper/Q2YCSMQ7"},"agent_actions":{"view_html":"https://pith.science/pith/Q2YCSMQ7AXOZSCBLSGN5XHH6XA","download_json":"https://pith.science/pith/Q2YCSMQ7AXOZSCBLSGN5XHH6XA.json","view_paper":"https://pith.science/paper/Q2YCSMQ7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1109.5684&json=true","fetch_graph":"https://pith.science/api/pith-number/Q2YCSMQ7AXOZSCBLSGN5XHH6XA/graph.json","fetch_events":"https://pith.science/api/pith-number/Q2YCSMQ7AXOZSCBLSGN5XHH6XA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/Q2YCSMQ7AXOZSCBLSGN5XHH6XA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/Q2YCSMQ7AXOZSCBLSGN5XHH6XA/action/storage_attestation","attest_author":"https://pith.science/pith/Q2YCSMQ7AXOZSCBLSGN5XHH6XA/action/author_attestation","sign_citation":"https://pith.science/pith/Q2YCSMQ7AXOZSCBLSGN5XHH6XA/action/citation_signature","submit_replication":"https://pith.science/pith/Q2YCSMQ7AXOZSCBLSGN5XHH6XA/action/replication_record"}},"created_at":"2026-05-18T03:11:33.728331+00:00","updated_at":"2026-05-18T03:11:33.728331+00:00"}