{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:EMYJOYE5BCQSC624MKB4E6H2S5","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"397b142673a0dd51ca40009a3300eef6dd22b854e74ca9a38be34256a7258447","cross_cats_sorted":["math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-01-09T13:24:59Z","title_canon_sha256":"53898c253aab56dff2a11842017ad9ea35a4c36c954b10986e369bf27a57fd73"},"schema_version":"1.0","source":{"id":"1201.1753","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1201.1753","created_at":"2026-05-18T02:56:45Z"},{"alias_kind":"arxiv_version","alias_value":"1201.1753v3","created_at":"2026-05-18T02:56:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.1753","created_at":"2026-05-18T02:56:45Z"},{"alias_kind":"pith_short_12","alias_value":"EMYJOYE5BCQS","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_16","alias_value":"EMYJOYE5BCQSC624","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_8","alias_value":"EMYJOYE5","created_at":"2026-05-18T12:27:04Z"}],"graph_snapshots":[{"event_id":"sha256:8aee67f23d5223d1d235c7e42c0f5e132d1eb3d49549cade302a4e55201016d6","target":"graph","created_at":"2026-05-18T02:56:45Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We extend, in the free probability framework, an invariance principle for multilinear homogeneous sums with low influences recently established in [E. Mossel, R. O'Donnell and K. Oleszkiewicz (2010). Noise stability of functions with low influences: invariance and optimality. {\\it Ann. Math.} {\\bf 171}, no. 1, 295-341]. To do so, a hypercontractivity property for those homogeneous sums is necessary, and to prove it has turned out to be our main task. Finally, we deduce from our extension several universality phenomenons, in the spirit of the paper [I. Nourdin, G. Peccati and G. Reinert (2010).","authors_text":"Aur\\'elien Deya (IECN), Ivan Nourdin (IECN)","cross_cats":["math.OA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-01-09T13:24:59Z","title":"Invariance principles for homogeneous sums of free random variables"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.1753","kind":"arxiv","version":3},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:b6f2d4fb2b7df1aaf8f6748465d299ae2c54c997e8c7da3cb03470465c0ebf7c","target":"record","created_at":"2026-05-18T02:56:45Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"397b142673a0dd51ca40009a3300eef6dd22b854e74ca9a38be34256a7258447","cross_cats_sorted":["math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-01-09T13:24:59Z","title_canon_sha256":"53898c253aab56dff2a11842017ad9ea35a4c36c954b10986e369bf27a57fd73"},"schema_version":"1.0","source":{"id":"1201.1753","kind":"arxiv","version":3}},"canonical_sha256":"233097609d08a1217b5c6283c278fa975fdf657568c736d638dade7942920b1c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"233097609d08a1217b5c6283c278fa975fdf657568c736d638dade7942920b1c","first_computed_at":"2026-05-18T02:56:45.207840Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:56:45.207840Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+lyHcQh5ZsM4VgCOCONyQWBX+uNBu7fhUKJgKP6sjuffjB7WoKcfeANIxWHQCPS53B02uXBUnW6mr6WLM9wxCg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:56:45.208308Z","signed_message":"canonical_sha256_bytes"},"source_id":"1201.1753","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b6f2d4fb2b7df1aaf8f6748465d299ae2c54c997e8c7da3cb03470465c0ebf7c","sha256:8aee67f23d5223d1d235c7e42c0f5e132d1eb3d49549cade302a4e55201016d6"],"state_sha256":"33faaf39a7875b6869048ff774deda33d258b3aaa49b8558be945acde0464452"}