{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:ZRIS3PLHXPJAME2FXKPTDXXVA4","short_pith_number":"pith:ZRIS3PLH","schema_version":"1.0","canonical_sha256":"cc512dbd67bbd2061345ba9f31def5070588c4fa0ee629b0e19c53a206d2e523","source":{"kind":"arxiv","id":"1409.5551","version":1},"attestation_state":"computed","paper":{"title":"Convergence towards linear combinations of chi-squared random variables: a Malliavin-based approach","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Ehsan Azmoodeh, Giovanni Peccati, Guillaume Poly","submitted_at":"2014-09-19T08:46:55Z","abstract_excerpt":"We investigate the problem of finding necessary and sufficient conditions for convergence in distribution towards a general finite linear combination of independent chi-squared random variables, within the framework of random objects living on a fixed Gaussian space. Using a recent representation of cumulants in terms of the Malliavin calculus operators $\\Gamma_i$ (introduced by Nourdin and Peccati in \\cite{n-pe-3}), we provide conditions that apply to random variables living in a finite sum of Wiener chaoses. As an important by-product of our analysis, we shall derive a new proof and a new 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":"1409.5551","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-09-19T08:46:55Z","cross_cats_sorted":[],"title_canon_sha256":"db066e3f377d65c1467efc5b60ea18cf4fccfffe9023cf6999079b7865df3225","abstract_canon_sha256":"a584265b1715f447f7b5368972e4a19e0321e3394784ca842d9f8c3d3bb1493f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:42:27.138389Z","signature_b64":"E9n3ris28Bca0aerXaRxk6xqN4hUEgqm3OzLrBc9oue0uJ3lTo+boWln9yKr39o6FUvbTAe+KJTfproP4DfXDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cc512dbd67bbd2061345ba9f31def5070588c4fa0ee629b0e19c53a206d2e523","last_reissued_at":"2026-05-18T02:42:27.137641Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:42:27.137641Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Convergence towards linear combinations of chi-squared random variables: a Malliavin-based approach","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Ehsan Azmoodeh, Giovanni Peccati, Guillaume Poly","submitted_at":"2014-09-19T08:46:55Z","abstract_excerpt":"We investigate the problem of finding necessary and sufficient conditions for convergence in distribution towards a general finite linear combination of independent chi-squared random variables, within the framework of random objects living on a fixed Gaussian space. Using a recent representation of cumulants in terms of the Malliavin calculus operators $\\Gamma_i$ (introduced by Nourdin and Peccati in \\cite{n-pe-3}), we provide conditions that apply to random variables living in a finite sum of Wiener chaoses. As an important by-product of our analysis, we shall derive a new proof and a new in"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.5551","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":"1409.5551","created_at":"2026-05-18T02:42:27.137751+00:00"},{"alias_kind":"arxiv_version","alias_value":"1409.5551v1","created_at":"2026-05-18T02:42:27.137751+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.5551","created_at":"2026-05-18T02:42:27.137751+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZRIS3PLHXPJA","created_at":"2026-05-18T12:28:59.999130+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZRIS3PLHXPJAME2F","created_at":"2026-05-18T12:28:59.999130+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZRIS3PLH","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/ZRIS3PLHXPJAME2FXKPTDXXVA4","json":"https://pith.science/pith/ZRIS3PLHXPJAME2FXKPTDXXVA4.json","graph_json":"https://pith.science/api/pith-number/ZRIS3PLHXPJAME2FXKPTDXXVA4/graph.json","events_json":"https://pith.science/api/pith-number/ZRIS3PLHXPJAME2FXKPTDXXVA4/events.json","paper":"https://pith.science/paper/ZRIS3PLH"},"agent_actions":{"view_html":"https://pith.science/pith/ZRIS3PLHXPJAME2FXKPTDXXVA4","download_json":"https://pith.science/pith/ZRIS3PLHXPJAME2FXKPTDXXVA4.json","view_paper":"https://pith.science/paper/ZRIS3PLH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1409.5551&json=true","fetch_graph":"https://pith.science/api/pith-number/ZRIS3PLHXPJAME2FXKPTDXXVA4/graph.json","fetch_events":"https://pith.science/api/pith-number/ZRIS3PLHXPJAME2FXKPTDXXVA4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZRIS3PLHXPJAME2FXKPTDXXVA4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZRIS3PLHXPJAME2FXKPTDXXVA4/action/storage_attestation","attest_author":"https://pith.science/pith/ZRIS3PLHXPJAME2FXKPTDXXVA4/action/author_attestation","sign_citation":"https://pith.science/pith/ZRIS3PLHXPJAME2FXKPTDXXVA4/action/citation_signature","submit_replication":"https://pith.science/pith/ZRIS3PLHXPJAME2FXKPTDXXVA4/action/replication_record"}},"created_at":"2026-05-18T02:42:27.137751+00:00","updated_at":"2026-05-18T02:42:27.137751+00:00"}