{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:RU4DGH6FLDLKVLJVFIL7YERVEV","short_pith_number":"pith:RU4DGH6F","schema_version":"1.0","canonical_sha256":"8d38331fc558d6aaad352a17fc1235257eaab5f82b48ca04ff8a6b52fc41c32d","source":{"kind":"arxiv","id":"1801.04109","version":2},"attestation_state":"computed","paper":{"title":"Couplings in $L^p$ distance of two Brownian motions and their L{\\'e}vy area","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Michel Bonnefont (IMB), Nicolas Juillet (IRMA)","submitted_at":"2018-01-12T09:48:17Z","abstract_excerpt":"We study co-adapted couplings of (canonical hypoelliptic) diffu-sions on the (subRiemannian) Heisenberg group, that we call (Heisenberg) Brow-nian motions and are the joint laws of a planar Brownian motion with its L{\\'e}vy area. We show that contrary to the situation observed on Riemannian manifolds of non-negative Ricci curvature, for any co-adapted coupling, two Heisenberg Brownian motions starting at two given points can not stay at bounded distance for all time t $\\ge$ 0. Actually, we prove the stronger result that they can not stay bounded in L p for p $\\ge$ 2. We also study the coupling"},"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":"1801.04109","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-01-12T09:48:17Z","cross_cats_sorted":[],"title_canon_sha256":"130d1360827f40676db8be95d32b8d6d26bf410e5bd10564a9977ca186df895b","abstract_canon_sha256":"644e7ba90bd7c2c1b2fbb53bae4635ec8754093f68d1a5e4d9cdc8746fc85d59"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:11:00.044774Z","signature_b64":"UKraynlJItjoFJ+mCPWzsWEeuq7GJPqy58Q0Dj4fQPqHWQQHsQPF4bqwhfTlXe1e5h4pKY8WdybI83xIzBjEDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8d38331fc558d6aaad352a17fc1235257eaab5f82b48ca04ff8a6b52fc41c32d","last_reissued_at":"2026-05-18T00:11:00.043281Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:11:00.043281Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Couplings in $L^p$ distance of two Brownian motions and their L{\\'e}vy area","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Michel Bonnefont (IMB), Nicolas Juillet (IRMA)","submitted_at":"2018-01-12T09:48:17Z","abstract_excerpt":"We study co-adapted couplings of (canonical hypoelliptic) diffu-sions on the (subRiemannian) Heisenberg group, that we call (Heisenberg) Brow-nian motions and are the joint laws of a planar Brownian motion with its L{\\'e}vy area. We show that contrary to the situation observed on Riemannian manifolds of non-negative Ricci curvature, for any co-adapted coupling, two Heisenberg Brownian motions starting at two given points can not stay at bounded distance for all time t $\\ge$ 0. Actually, we prove the stronger result that they can not stay bounded in L p for p $\\ge$ 2. We also study the coupling"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.04109","kind":"arxiv","version":2},"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":"1801.04109","created_at":"2026-05-18T00:11:00.044052+00:00"},{"alias_kind":"arxiv_version","alias_value":"1801.04109v2","created_at":"2026-05-18T00:11:00.044052+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.04109","created_at":"2026-05-18T00:11:00.044052+00:00"},{"alias_kind":"pith_short_12","alias_value":"RU4DGH6FLDLK","created_at":"2026-05-18T12:32:50.500415+00:00"},{"alias_kind":"pith_short_16","alias_value":"RU4DGH6FLDLKVLJV","created_at":"2026-05-18T12:32:50.500415+00:00"},{"alias_kind":"pith_short_8","alias_value":"RU4DGH6F","created_at":"2026-05-18T12:32:50.500415+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/RU4DGH6FLDLKVLJVFIL7YERVEV","json":"https://pith.science/pith/RU4DGH6FLDLKVLJVFIL7YERVEV.json","graph_json":"https://pith.science/api/pith-number/RU4DGH6FLDLKVLJVFIL7YERVEV/graph.json","events_json":"https://pith.science/api/pith-number/RU4DGH6FLDLKVLJVFIL7YERVEV/events.json","paper":"https://pith.science/paper/RU4DGH6F"},"agent_actions":{"view_html":"https://pith.science/pith/RU4DGH6FLDLKVLJVFIL7YERVEV","download_json":"https://pith.science/pith/RU4DGH6FLDLKVLJVFIL7YERVEV.json","view_paper":"https://pith.science/paper/RU4DGH6F","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1801.04109&json=true","fetch_graph":"https://pith.science/api/pith-number/RU4DGH6FLDLKVLJVFIL7YERVEV/graph.json","fetch_events":"https://pith.science/api/pith-number/RU4DGH6FLDLKVLJVFIL7YERVEV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/RU4DGH6FLDLKVLJVFIL7YERVEV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/RU4DGH6FLDLKVLJVFIL7YERVEV/action/storage_attestation","attest_author":"https://pith.science/pith/RU4DGH6FLDLKVLJVFIL7YERVEV/action/author_attestation","sign_citation":"https://pith.science/pith/RU4DGH6FLDLKVLJVFIL7YERVEV/action/citation_signature","submit_replication":"https://pith.science/pith/RU4DGH6FLDLKVLJVFIL7YERVEV/action/replication_record"}},"created_at":"2026-05-18T00:11:00.044052+00:00","updated_at":"2026-05-18T00:11:00.044052+00:00"}