{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:FQ5TNPS4HL327JPEJFR5UQUSNV","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":"c02f73eedd2fcfb17cd8c2da651f93e47c5ba867a22ca0b6f3bc7129dd25a5e2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-03-09T07:33:30Z","title_canon_sha256":"a729a4e583084086e66ef82c8c05a2694adfac4ff3f011725626a2f5cb733431"},"schema_version":"1.0","source":{"id":"1203.2007","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1203.2007","created_at":"2026-05-18T04:00:27Z"},{"alias_kind":"arxiv_version","alias_value":"1203.2007v1","created_at":"2026-05-18T04:00:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.2007","created_at":"2026-05-18T04:00:27Z"},{"alias_kind":"pith_short_12","alias_value":"FQ5TNPS4HL32","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_16","alias_value":"FQ5TNPS4HL327JPE","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_8","alias_value":"FQ5TNPS4","created_at":"2026-05-18T12:27:06Z"}],"graph_snapshots":[{"event_id":"sha256:c208c73f1f70842f757c1b8731a019dbeb9482d99a570b5f7d9c072729ae6c03","target":"graph","created_at":"2026-05-18T04:00:27Z","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":"The asymptotic shape theorem for the contact process in random environment gives the existence of a norm $\\mu$ on $\\Rd$ such that the hitting time $t(x)$ is asymptotically equivalent to $\\mu(x)$ when the contact process survives. We provide here exponential upper bounds for the probability of the event $\\{\\frac{t(x)}{\\mu(x)}\\not\\in [1-\\epsilon,1+\\epsilon]\\}$; these bounds are optimal for independent random environment. As a special case, this gives the large deviation inequality for the contact process in a deterministic environment, which, as far as we know, has not been established yet.","authors_text":"Olivier Garet (IECN), R\\'egine Marchand (IECN)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-03-09T07:33:30Z","title":"Large deviations for the contact process in random environment"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.2007","kind":"arxiv","version":1},"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:b71093ee8c3d5aaa21c18f2f04bc36f4d6f9973824dc2c29f47968ef2c16da1b","target":"record","created_at":"2026-05-18T04:00:27Z","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":"c02f73eedd2fcfb17cd8c2da651f93e47c5ba867a22ca0b6f3bc7129dd25a5e2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-03-09T07:33:30Z","title_canon_sha256":"a729a4e583084086e66ef82c8c05a2694adfac4ff3f011725626a2f5cb733431"},"schema_version":"1.0","source":{"id":"1203.2007","kind":"arxiv","version":1}},"canonical_sha256":"2c3b36be5c3af7afa5e44963da42926d53ab02926ddcd48802d77443f6849e86","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2c3b36be5c3af7afa5e44963da42926d53ab02926ddcd48802d77443f6849e86","first_computed_at":"2026-05-18T04:00:27.723975Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:00:27.723975Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"N55pc/Nm15AH6T36jbuRdesbZkR4PIcMoxZbEtcjp5KgPm0jtCb8R5+BbpBBMD8X8IuqF7l3aZWcgbD/KvhuBw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:00:27.724708Z","signed_message":"canonical_sha256_bytes"},"source_id":"1203.2007","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b71093ee8c3d5aaa21c18f2f04bc36f4d6f9973824dc2c29f47968ef2c16da1b","sha256:c208c73f1f70842f757c1b8731a019dbeb9482d99a570b5f7d9c072729ae6c03"],"state_sha256":"bd2d5b8377fdbf633b54b90ddbc213bf585e418d79e7b34f6dc2b9465f1a593b"}