{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:FI2NHRGDPOEDZ4Z5PPRPZNMZ25","short_pith_number":"pith:FI2NHRGD","schema_version":"1.0","canonical_sha256":"2a34d3c4c37b883cf33d7be2fcb599d75b3d900cacf6235fc67a040e496c386a","source":{"kind":"arxiv","id":"1802.06282","version":6},"attestation_state":"computed","paper":{"title":"Large Rank-Based Models with Common Noise","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Andrey Sarantsev, Praveen Kolli","submitted_at":"2018-02-17T20:05:46Z","abstract_excerpt":"For large systems of Brownian particles interacting through their ranks introduced in (Banner, Fernholz, Karatzas, 2005), the empirical cumulative distribution function satisfies a porous medium PDE. However, when we introduce a common noise, the limit is no longer deterministic. Instead, we show that this limit is a solution of a stochastic PDE related to this porous medium PDE. This stochastic PDE is somewhat similar to the equations developed for conservation laws with rough stochastic fluxes (Lions, Perthame, Souganidis, 2013)."},"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":"1802.06282","kind":"arxiv","version":6},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-02-17T20:05:46Z","cross_cats_sorted":[],"title_canon_sha256":"b7a482626e449170aaf49135582dbadf0f7b84c357c792f0d136614d804b2be8","abstract_canon_sha256":"011eed1fa6331167f66d41dd382622faf665f31096a6680231f7f8c88c513ec1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:46:36.377815Z","signature_b64":"qfRuovZv8MEd2rf4DGlwimomow35mR/5xUg62u/fvJ12/fX4T/G00nKNAi+NrUa0WpQ4TKhtiK/T8OYvA9d6Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2a34d3c4c37b883cf33d7be2fcb599d75b3d900cacf6235fc67a040e496c386a","last_reissued_at":"2026-05-17T23:46:36.377285Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:46:36.377285Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Large Rank-Based Models with Common Noise","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Andrey Sarantsev, Praveen Kolli","submitted_at":"2018-02-17T20:05:46Z","abstract_excerpt":"For large systems of Brownian particles interacting through their ranks introduced in (Banner, Fernholz, Karatzas, 2005), the empirical cumulative distribution function satisfies a porous medium PDE. However, when we introduce a common noise, the limit is no longer deterministic. Instead, we show that this limit is a solution of a stochastic PDE related to this porous medium PDE. This stochastic PDE is somewhat similar to the equations developed for conservation laws with rough stochastic fluxes (Lions, Perthame, Souganidis, 2013)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.06282","kind":"arxiv","version":6},"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":"1802.06282","created_at":"2026-05-17T23:46:36.377379+00:00"},{"alias_kind":"arxiv_version","alias_value":"1802.06282v6","created_at":"2026-05-17T23:46:36.377379+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.06282","created_at":"2026-05-17T23:46:36.377379+00:00"},{"alias_kind":"pith_short_12","alias_value":"FI2NHRGDPOED","created_at":"2026-05-18T12:32:22.470017+00:00"},{"alias_kind":"pith_short_16","alias_value":"FI2NHRGDPOEDZ4Z5","created_at":"2026-05-18T12:32:22.470017+00:00"},{"alias_kind":"pith_short_8","alias_value":"FI2NHRGD","created_at":"2026-05-18T12:32:22.470017+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/FI2NHRGDPOEDZ4Z5PPRPZNMZ25","json":"https://pith.science/pith/FI2NHRGDPOEDZ4Z5PPRPZNMZ25.json","graph_json":"https://pith.science/api/pith-number/FI2NHRGDPOEDZ4Z5PPRPZNMZ25/graph.json","events_json":"https://pith.science/api/pith-number/FI2NHRGDPOEDZ4Z5PPRPZNMZ25/events.json","paper":"https://pith.science/paper/FI2NHRGD"},"agent_actions":{"view_html":"https://pith.science/pith/FI2NHRGDPOEDZ4Z5PPRPZNMZ25","download_json":"https://pith.science/pith/FI2NHRGDPOEDZ4Z5PPRPZNMZ25.json","view_paper":"https://pith.science/paper/FI2NHRGD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1802.06282&json=true","fetch_graph":"https://pith.science/api/pith-number/FI2NHRGDPOEDZ4Z5PPRPZNMZ25/graph.json","fetch_events":"https://pith.science/api/pith-number/FI2NHRGDPOEDZ4Z5PPRPZNMZ25/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FI2NHRGDPOEDZ4Z5PPRPZNMZ25/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FI2NHRGDPOEDZ4Z5PPRPZNMZ25/action/storage_attestation","attest_author":"https://pith.science/pith/FI2NHRGDPOEDZ4Z5PPRPZNMZ25/action/author_attestation","sign_citation":"https://pith.science/pith/FI2NHRGDPOEDZ4Z5PPRPZNMZ25/action/citation_signature","submit_replication":"https://pith.science/pith/FI2NHRGDPOEDZ4Z5PPRPZNMZ25/action/replication_record"}},"created_at":"2026-05-17T23:46:36.377379+00:00","updated_at":"2026-05-17T23:46:36.377379+00:00"}