{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:V3SD3VZCLZUQ5RQEU7AGV2SZ73","short_pith_number":"pith:V3SD3VZC","schema_version":"1.0","canonical_sha256":"aee43dd7225e690ec604a7c06aea59fee22c6e2fbf6b12322e4cf8e702da0286","source":{"kind":"arxiv","id":"1706.00121","version":2},"attestation_state":"computed","paper":{"title":"Concentration inequalities for polynomials of contracting Ising models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Eyal Lubetzky, Reza Gheissari, Yuval Peres","submitted_at":"2017-05-31T23:19:55Z","abstract_excerpt":"We study the concentration of a degree-$d$ polynomial of the $N$ spins of a general Ising model, in the regime where single-site Glauber dynamics is contracting. For $d=1$, Gaussian concentration was shown by Marton (1996) and Samson (2000) as a special case of concentration for convex Lipschitz functions, and extended to a variety of related settings by e.g., Chazottes et al. (2007) and Kontorovich and Ramanan (2008). For $d=2$, exponential concentration was shown by Marton (2003) on lattices. We treat a general fixed degree $d$ with $O(1)$ coefficients, and show that the polynomial has varia"},"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":"1706.00121","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-05-31T23:19:55Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"aace9adb5e2c986528ada54af9a500169dc7cb335225d32713a1a69ad72e9a1d","abstract_canon_sha256":"b9cf12172e9df47dfad6fd9e8c1b34356ab09aa29d353a8dacf9dd063cd5b841"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:36:13.988818Z","signature_b64":"Y80qe0a7kfaxa+Lg32zJ27Wz7C46kYcRX893L4A7m8+rbN6F3PK9glzJTufYiZUvFsjStcQKa48+NSeAztprBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"aee43dd7225e690ec604a7c06aea59fee22c6e2fbf6b12322e4cf8e702da0286","last_reissued_at":"2026-05-18T00:36:13.987935Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:36:13.987935Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Concentration inequalities for polynomials of contracting Ising models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Eyal Lubetzky, Reza Gheissari, Yuval Peres","submitted_at":"2017-05-31T23:19:55Z","abstract_excerpt":"We study the concentration of a degree-$d$ polynomial of the $N$ spins of a general Ising model, in the regime where single-site Glauber dynamics is contracting. For $d=1$, Gaussian concentration was shown by Marton (1996) and Samson (2000) as a special case of concentration for convex Lipschitz functions, and extended to a variety of related settings by e.g., Chazottes et al. (2007) and Kontorovich and Ramanan (2008). For $d=2$, exponential concentration was shown by Marton (2003) on lattices. We treat a general fixed degree $d$ with $O(1)$ coefficients, and show that the polynomial has varia"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.00121","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":"1706.00121","created_at":"2026-05-18T00:36:13.988083+00:00"},{"alias_kind":"arxiv_version","alias_value":"1706.00121v2","created_at":"2026-05-18T00:36:13.988083+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.00121","created_at":"2026-05-18T00:36:13.988083+00:00"},{"alias_kind":"pith_short_12","alias_value":"V3SD3VZCLZUQ","created_at":"2026-05-18T12:31:49.984773+00:00"},{"alias_kind":"pith_short_16","alias_value":"V3SD3VZCLZUQ5RQE","created_at":"2026-05-18T12:31:49.984773+00:00"},{"alias_kind":"pith_short_8","alias_value":"V3SD3VZC","created_at":"2026-05-18T12:31:49.984773+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"1906.09247","citing_title":"Learning from weakly dependent data under Dobrushin's condition","ref_index":16,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/V3SD3VZCLZUQ5RQEU7AGV2SZ73","json":"https://pith.science/pith/V3SD3VZCLZUQ5RQEU7AGV2SZ73.json","graph_json":"https://pith.science/api/pith-number/V3SD3VZCLZUQ5RQEU7AGV2SZ73/graph.json","events_json":"https://pith.science/api/pith-number/V3SD3VZCLZUQ5RQEU7AGV2SZ73/events.json","paper":"https://pith.science/paper/V3SD3VZC"},"agent_actions":{"view_html":"https://pith.science/pith/V3SD3VZCLZUQ5RQEU7AGV2SZ73","download_json":"https://pith.science/pith/V3SD3VZCLZUQ5RQEU7AGV2SZ73.json","view_paper":"https://pith.science/paper/V3SD3VZC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1706.00121&json=true","fetch_graph":"https://pith.science/api/pith-number/V3SD3VZCLZUQ5RQEU7AGV2SZ73/graph.json","fetch_events":"https://pith.science/api/pith-number/V3SD3VZCLZUQ5RQEU7AGV2SZ73/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/V3SD3VZCLZUQ5RQEU7AGV2SZ73/action/timestamp_anchor","attest_storage":"https://pith.science/pith/V3SD3VZCLZUQ5RQEU7AGV2SZ73/action/storage_attestation","attest_author":"https://pith.science/pith/V3SD3VZCLZUQ5RQEU7AGV2SZ73/action/author_attestation","sign_citation":"https://pith.science/pith/V3SD3VZCLZUQ5RQEU7AGV2SZ73/action/citation_signature","submit_replication":"https://pith.science/pith/V3SD3VZCLZUQ5RQEU7AGV2SZ73/action/replication_record"}},"created_at":"2026-05-18T00:36:13.988083+00:00","updated_at":"2026-05-18T00:36:13.988083+00:00"}