{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:JB4HL7MN72ILXTQDM6QZL3QJTL","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"07aa5a75849f6f91e7f97388618b0ac452995426b8132f6f8d837ee367b6f9e7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-07-15T22:30:06Z","title_canon_sha256":"f6212c9e357a96ee90dcb94d0e4d0b5d84d2ab5904c59e9c577e203dca1501e7"},"schema_version":"1.0","source":{"id":"1007.2669","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1007.2669","created_at":"2026-05-18T03:30:54Z"},{"alias_kind":"arxiv_version","alias_value":"1007.2669v3","created_at":"2026-05-18T03:30:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1007.2669","created_at":"2026-05-18T03:30:54Z"},{"alias_kind":"pith_short_12","alias_value":"JB4HL7MN72IL","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_16","alias_value":"JB4HL7MN72ILXTQD","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_8","alias_value":"JB4HL7MN","created_at":"2026-05-18T12:26:09Z"}],"graph_snapshots":[{"event_id":"sha256:65ca04e21cab95b1a50110c24222766e823732449a0691571526122d4519c8a4","target":"graph","created_at":"2026-05-18T03:30:54Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We prove an upper bound for the $\\varepsilon$-mixing time of the symmetric exclusion process on any graph G, with any feasible number of particles. Our estimate is proportional to $\\mathsf{T}_{\\mathsf{RW}(G)}\\ln(|V|/\\varepsilon)$, where |V| is the number of vertices in G, and $\\mathsf{T}_{\\mathsf{RW}(G)}$ is the 1/4-mixing time of the corresponding single-particle random walk. This bound implies new results for symmetric exclusion on expanders, percolation clusters, the giant component of the Erdos-Renyi random graph and Poisson point processes in $\\mathbb{R}^d$. Our technical tools include a ","authors_text":"Roberto Imbuzeiro Oliveira","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-07-15T22:30:06Z","title":"Mixing of the symmetric exclusion processes in terms of the corresponding single-particle random walk"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1007.2669","kind":"arxiv","version":3},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:0176c95477a72e99c8b37cbb32c587a45f5df72a94184a1a842592a5ecba4af8","target":"record","created_at":"2026-05-18T03:30:54Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"07aa5a75849f6f91e7f97388618b0ac452995426b8132f6f8d837ee367b6f9e7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-07-15T22:30:06Z","title_canon_sha256":"f6212c9e357a96ee90dcb94d0e4d0b5d84d2ab5904c59e9c577e203dca1501e7"},"schema_version":"1.0","source":{"id":"1007.2669","kind":"arxiv","version":3}},"canonical_sha256":"487875fd8dfe90bbce0367a195ee099ace61873383b1fca53a9ef86da35a8c41","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"487875fd8dfe90bbce0367a195ee099ace61873383b1fca53a9ef86da35a8c41","first_computed_at":"2026-05-18T03:30:54.105898Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:30:54.105898Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ebKiQOFLGWzOz/gwjRnk+pMp7ok3MUKD0xei/p877bBBcx9nuesFrCEuyyBy+aPdm9xZBafBPChUmeJSQZTZDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:30:54.106703Z","signed_message":"canonical_sha256_bytes"},"source_id":"1007.2669","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0176c95477a72e99c8b37cbb32c587a45f5df72a94184a1a842592a5ecba4af8","sha256:65ca04e21cab95b1a50110c24222766e823732449a0691571526122d4519c8a4"],"state_sha256":"c2355769f18d6fa43f2ace9ca74894e570c382960ac638ee32f2f2d33ca55660"}