{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:ZBYMHOWVNW3ROXIFJRQOPAYSV2","short_pith_number":"pith:ZBYMHOWV","schema_version":"1.0","canonical_sha256":"c870c3bad56db7175d054c60e78312ae939c2a101d50ce4c6de805607be2dccd","source":{"kind":"arxiv","id":"1401.2247","version":1},"attestation_state":"computed","paper":{"title":"Strong asymptotic independence on Wiener chaos","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"David Nualart, Giovanni Peccati (FSTC), Ivan Nourdin (IECL)","submitted_at":"2014-01-10T08:06:57Z","abstract_excerpt":"Let $F_n = (F_{1,n}, ....,F_{d,n})$, $n\\geq 1$, be a sequence of random vectors such that, for every $j=1,...,d$, the random variable $F_{j,n}$ belongs to a fixed Wiener chaos of a Gaussian field. We show that, as $n\\to\\infty$, the components of $F_n$ are asymptotically independent if and only if ${\\rm Cov}(F_{i,n}^2,F_{j,n}^2)\\to 0$ for every $i\\neq j$. Our findings are based on a novel inequality for vectors of multiple Wiener-It\\^o integrals, and represent a substantial refining of criteria for asymptotic independence in the sense of moments recently established by Nourdin and Rosinski."},"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":"1401.2247","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-01-10T08:06:57Z","cross_cats_sorted":[],"title_canon_sha256":"aac4774e1c357de4e269997321630bee5b49d65994dcf45194435b87c42f5a81","abstract_canon_sha256":"816e7c63dd567157a7a346b7e402d7657c32f398465bab81c839d1154bc81b6f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:02:45.907932Z","signature_b64":"t0wkS+xljvpy+p8GhNFyjHWVaxdHCZ46hCni3/rgwbNP/vCShEeT5Wm03sPXwWrSmKT5fQyN/A/XdFliXRgxAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c870c3bad56db7175d054c60e78312ae939c2a101d50ce4c6de805607be2dccd","last_reissued_at":"2026-05-18T03:02:45.907325Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:02:45.907325Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Strong asymptotic independence on Wiener chaos","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"David Nualart, Giovanni Peccati (FSTC), Ivan Nourdin (IECL)","submitted_at":"2014-01-10T08:06:57Z","abstract_excerpt":"Let $F_n = (F_{1,n}, ....,F_{d,n})$, $n\\geq 1$, be a sequence of random vectors such that, for every $j=1,...,d$, the random variable $F_{j,n}$ belongs to a fixed Wiener chaos of a Gaussian field. We show that, as $n\\to\\infty$, the components of $F_n$ are asymptotically independent if and only if ${\\rm Cov}(F_{i,n}^2,F_{j,n}^2)\\to 0$ for every $i\\neq j$. Our findings are based on a novel inequality for vectors of multiple Wiener-It\\^o integrals, and represent a substantial refining of criteria for asymptotic independence in the sense of moments recently established by Nourdin and Rosinski."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.2247","kind":"arxiv","version":1},"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":"1401.2247","created_at":"2026-05-18T03:02:45.907407+00:00"},{"alias_kind":"arxiv_version","alias_value":"1401.2247v1","created_at":"2026-05-18T03:02:45.907407+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.2247","created_at":"2026-05-18T03:02:45.907407+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZBYMHOWVNW3R","created_at":"2026-05-18T12:28:59.999130+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZBYMHOWVNW3ROXIF","created_at":"2026-05-18T12:28:59.999130+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZBYMHOWV","created_at":"2026-05-18T12:28:59.999130+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/ZBYMHOWVNW3ROXIFJRQOPAYSV2","json":"https://pith.science/pith/ZBYMHOWVNW3ROXIFJRQOPAYSV2.json","graph_json":"https://pith.science/api/pith-number/ZBYMHOWVNW3ROXIFJRQOPAYSV2/graph.json","events_json":"https://pith.science/api/pith-number/ZBYMHOWVNW3ROXIFJRQOPAYSV2/events.json","paper":"https://pith.science/paper/ZBYMHOWV"},"agent_actions":{"view_html":"https://pith.science/pith/ZBYMHOWVNW3ROXIFJRQOPAYSV2","download_json":"https://pith.science/pith/ZBYMHOWVNW3ROXIFJRQOPAYSV2.json","view_paper":"https://pith.science/paper/ZBYMHOWV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1401.2247&json=true","fetch_graph":"https://pith.science/api/pith-number/ZBYMHOWVNW3ROXIFJRQOPAYSV2/graph.json","fetch_events":"https://pith.science/api/pith-number/ZBYMHOWVNW3ROXIFJRQOPAYSV2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZBYMHOWVNW3ROXIFJRQOPAYSV2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZBYMHOWVNW3ROXIFJRQOPAYSV2/action/storage_attestation","attest_author":"https://pith.science/pith/ZBYMHOWVNW3ROXIFJRQOPAYSV2/action/author_attestation","sign_citation":"https://pith.science/pith/ZBYMHOWVNW3ROXIFJRQOPAYSV2/action/citation_signature","submit_replication":"https://pith.science/pith/ZBYMHOWVNW3ROXIFJRQOPAYSV2/action/replication_record"}},"created_at":"2026-05-18T03:02:45.907407+00:00","updated_at":"2026-05-18T03:02:45.907407+00:00"}