{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:ZKSHIR4EZDYXPUHE7IXCLLLAI4","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":"2e71e65fdf1a7b6f22411953aad38caba6f6ebab9ea1dbbb47eec9c41e4cb312","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-01-13T11:41:21Z","title_canon_sha256":"4028fa3f5fe6826ea36993422c727de36c574ce6848af37553f295db901d5c0f"},"schema_version":"1.0","source":{"id":"1401.2798","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.2798","created_at":"2026-05-18T02:05:24Z"},{"alias_kind":"arxiv_version","alias_value":"1401.2798v2","created_at":"2026-05-18T02:05:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.2798","created_at":"2026-05-18T02:05:24Z"},{"alias_kind":"pith_short_12","alias_value":"ZKSHIR4EZDYX","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_16","alias_value":"ZKSHIR4EZDYXPUHE","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_8","alias_value":"ZKSHIR4E","created_at":"2026-05-18T12:28:59Z"}],"graph_snapshots":[{"event_id":"sha256:c0bb2c8b135650c6b1c3b629359847ded4600b92bc699ec845f0e5c5b884dccc","target":"graph","created_at":"2026-05-18T02:05:24Z","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":"In this paper we study the Large Deviation Principle (LDP in abbreviation) for a class of Stochastic Partial Differential Equations (SPDEs) in the whole space $\\mathbb{R}^d$, with arbitrary dimension $d\\geq 1$, under random influence which is a Gaussian noise, white in time and correlated in space. The differential operator is a fractional derivative operator. We prove a large deviations principle for our equation, using a weak convergence approach based on a variational representation of functionals of infinite-dimensional Brownian motion. This approach reduces the proof of LDP to establishin","authors_text":"Mohamed Mellouk, Tarik El Mellali","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-01-13T11:41:21Z","title":"Large deviations for a fractional stochastic heat equation in spatial dimension $\\mathbb{R}^d$ driven by a spatially correlated noise"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.2798","kind":"arxiv","version":2},"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:b8e65b62d8c21fa7d132176bc6748f72c41e0ebbdedf69e51bb43a7d05ca5c0e","target":"record","created_at":"2026-05-18T02:05:24Z","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":"2e71e65fdf1a7b6f22411953aad38caba6f6ebab9ea1dbbb47eec9c41e4cb312","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-01-13T11:41:21Z","title_canon_sha256":"4028fa3f5fe6826ea36993422c727de36c574ce6848af37553f295db901d5c0f"},"schema_version":"1.0","source":{"id":"1401.2798","kind":"arxiv","version":2}},"canonical_sha256":"caa4744784c8f177d0e4fa2e25ad604734768cf154f54dd955b9ff4681122acf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"caa4744784c8f177d0e4fa2e25ad604734768cf154f54dd955b9ff4681122acf","first_computed_at":"2026-05-18T02:05:24.547110Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:05:24.547110Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Eekh4Ilm+p113lo4fNNE8OAUw33GKV51Kl5cIqQB4KeufBErBZOkfnhL6fKkrfcAws+iHDMeF/bsqqi/qICXAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:05:24.547833Z","signed_message":"canonical_sha256_bytes"},"source_id":"1401.2798","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b8e65b62d8c21fa7d132176bc6748f72c41e0ebbdedf69e51bb43a7d05ca5c0e","sha256:c0bb2c8b135650c6b1c3b629359847ded4600b92bc699ec845f0e5c5b884dccc"],"state_sha256":"73dc6907f8ed1660e50b434fccbfcf173f0f89b6c773b882ad4f964a4d50cde4"}