{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:5D2BMQ443OUQM3CJZ6JYSV7NNY","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":"3f127c0afc6943454a44b508edad88d423075702d90e5df8df6842739ebfbf63","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-09-23T20:27:58Z","title_canon_sha256":"14c8f5774364d362e257a09ab7cd588792b060607c1b456654dd47fa6bbc4a71"},"schema_version":"1.0","source":{"id":"1109.5193","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.5193","created_at":"2026-05-18T03:54:04Z"},{"alias_kind":"arxiv_version","alias_value":"1109.5193v2","created_at":"2026-05-18T03:54:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.5193","created_at":"2026-05-18T03:54:04Z"},{"alias_kind":"pith_short_12","alias_value":"5D2BMQ443OUQ","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_16","alias_value":"5D2BMQ443OUQM3CJ","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_8","alias_value":"5D2BMQ44","created_at":"2026-05-18T12:26:20Z"}],"graph_snapshots":[{"event_id":"sha256:09c4ded9ad6b07d53fbfe4fa3f3fdce0167e01129811ad7959705a48c773dd1b","target":"graph","created_at":"2026-05-18T03:54:04Z","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 show that the probability that a multilinear polynomial $f$ of independent random variables exceeds its mean by $\\lambda$ is at most $e^{-\\lambda^2 / (R^q Var(f))}$ for sufficiently small $\\lambda$, where $R$ is an absolute constant. This matches (up to constants in the exponent) what one would expect from the central limit theorem. Our methods handle a variety of types of random variables including Gaussian, Boolean, exponential, and Poisson. Previous work by Kim-Vu and Schudy-Sviridenko gave bounds of the same form that involved less natural parameters in place of the variance.","authors_text":"Maxim Sviridenko, Warren Schudy","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-09-23T20:27:58Z","title":"Bernstein-like Concentration and Moment Inequalities for Polynomials of Independent Random Variables: Multilinear Case"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.5193","kind":"arxiv","version":2},"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:a7862bf6145bffd35df6adddfd376db925889de7eebc30ea302e23f2d58737f2","target":"record","created_at":"2026-05-18T03:54:04Z","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":"3f127c0afc6943454a44b508edad88d423075702d90e5df8df6842739ebfbf63","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-09-23T20:27:58Z","title_canon_sha256":"14c8f5774364d362e257a09ab7cd588792b060607c1b456654dd47fa6bbc4a71"},"schema_version":"1.0","source":{"id":"1109.5193","kind":"arxiv","version":2}},"canonical_sha256":"e8f416439cdba9066c49cf938957ed6e1f58e3da7cc7990edc29fc011f14465d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e8f416439cdba9066c49cf938957ed6e1f58e3da7cc7990edc29fc011f14465d","first_computed_at":"2026-05-18T03:54:04.378055Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:54:04.378055Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"e77OKusasMjVKN0d2MgvY0TbxC5+Ciz6VDk0wkb+jKvAQ2BG75Z0BsKVd3VAxMmuj+EGXWG0vFYUqm9Xfgv3Cw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:54:04.378669Z","signed_message":"canonical_sha256_bytes"},"source_id":"1109.5193","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a7862bf6145bffd35df6adddfd376db925889de7eebc30ea302e23f2d58737f2","sha256:09c4ded9ad6b07d53fbfe4fa3f3fdce0167e01129811ad7959705a48c773dd1b"],"state_sha256":"268661b26bc1a2400a483a50b2f24b8082334ac2557f8e109314a1caadc622e8"}