{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:Q52HBXHXAHCDBYDJEN5DGIL7DM","short_pith_number":"pith:Q52HBXHX","schema_version":"1.0","canonical_sha256":"877470dcf701c430e069237a33217f1b2360222cb8d2d618d914809e4ae1d683","source":{"kind":"arxiv","id":"2306.16130","version":3},"attestation_state":"computed","paper":{"title":"A note on the Long-Time behaviour of Stochastic McKean-Vlasov Equations with common noise","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.AP","authors_text":"Raphael Maillet (CEREMADE)","submitted_at":"2023-06-28T11:59:59Z","abstract_excerpt":"This paper focuses on the long-term behavior of solutions to nonlinear stochastic Fokker-Planck equations driven by common noise, where the drift term has a linear dependence on the measure. These equations, which describe the evolution of probability distributions, naturally arise in the mean-field limit of interacting particle systems driven by both idiosyncratic and common noises. After proving the existence of an invariant measure under some mild conditions, we first consider the case where the confinement potential is uniformly convex. In this setting, we establish a result of uniform-in-"},"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":"2306.16130","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2023-06-28T11:59:59Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"adcd22e940a545096bae9d0fa0da53cd86d7f4c11832754cd3199b0c7b654680","abstract_canon_sha256":"ac6da1da3942989803105833f1be0f4e34ca3cb89c4cf73ee92323b0288c4474"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:25:02.779252Z","signature_b64":"aNx/wk/TTy31RXI+WKMwGVNac2ROkht7Eumi0mlGUhmfkA5PM2gbn2Nsop3iJYR0WyjdalY572XYWzCOga5aDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"877470dcf701c430e069237a33217f1b2360222cb8d2d618d914809e4ae1d683","last_reissued_at":"2026-07-05T10:25:02.778839Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:25:02.778839Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A note on the Long-Time behaviour of Stochastic McKean-Vlasov Equations with common noise","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.AP","authors_text":"Raphael Maillet (CEREMADE)","submitted_at":"2023-06-28T11:59:59Z","abstract_excerpt":"This paper focuses on the long-term behavior of solutions to nonlinear stochastic Fokker-Planck equations driven by common noise, where the drift term has a linear dependence on the measure. These equations, which describe the evolution of probability distributions, naturally arise in the mean-field limit of interacting particle systems driven by both idiosyncratic and common noises. After proving the existence of an invariant measure under some mild conditions, we first consider the case where the confinement potential is uniformly convex. In this setting, we establish a result of uniform-in-"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2306.16130","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2306.16130/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2306.16130","created_at":"2026-07-05T10:25:02.778899+00:00"},{"alias_kind":"arxiv_version","alias_value":"2306.16130v3","created_at":"2026-07-05T10:25:02.778899+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2306.16130","created_at":"2026-07-05T10:25:02.778899+00:00"},{"alias_kind":"pith_short_12","alias_value":"Q52HBXHXAHCD","created_at":"2026-07-05T10:25:02.778899+00:00"},{"alias_kind":"pith_short_16","alias_value":"Q52HBXHXAHCDBYDJ","created_at":"2026-07-05T10:25:02.778899+00:00"},{"alias_kind":"pith_short_8","alias_value":"Q52HBXHX","created_at":"2026-07-05T10:25:02.778899+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":2,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2606.30000","citing_title":"Adaptive nonparametric regression from repeated measurements under common noise","ref_index":20,"is_internal_anchor":false},{"citing_arxiv_id":"2605.11785","citing_title":"Regularization of a mean-field SDE by an additive common noise: The conditional expectation case","ref_index":25,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/Q52HBXHXAHCDBYDJEN5DGIL7DM","json":"https://pith.science/pith/Q52HBXHXAHCDBYDJEN5DGIL7DM.json","graph_json":"https://pith.science/api/pith-number/Q52HBXHXAHCDBYDJEN5DGIL7DM/graph.json","events_json":"https://pith.science/api/pith-number/Q52HBXHXAHCDBYDJEN5DGIL7DM/events.json","paper":"https://pith.science/paper/Q52HBXHX"},"agent_actions":{"view_html":"https://pith.science/pith/Q52HBXHXAHCDBYDJEN5DGIL7DM","download_json":"https://pith.science/pith/Q52HBXHXAHCDBYDJEN5DGIL7DM.json","view_paper":"https://pith.science/paper/Q52HBXHX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2306.16130&json=true","fetch_graph":"https://pith.science/api/pith-number/Q52HBXHXAHCDBYDJEN5DGIL7DM/graph.json","fetch_events":"https://pith.science/api/pith-number/Q52HBXHXAHCDBYDJEN5DGIL7DM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/Q52HBXHXAHCDBYDJEN5DGIL7DM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/Q52HBXHXAHCDBYDJEN5DGIL7DM/action/storage_attestation","attest_author":"https://pith.science/pith/Q52HBXHXAHCDBYDJEN5DGIL7DM/action/author_attestation","sign_citation":"https://pith.science/pith/Q52HBXHXAHCDBYDJEN5DGIL7DM/action/citation_signature","submit_replication":"https://pith.science/pith/Q52HBXHXAHCDBYDJEN5DGIL7DM/action/replication_record"}},"created_at":"2026-07-05T10:25:02.778899+00:00","updated_at":"2026-07-05T10:25:02.778899+00:00"}