{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:ZAUCVZD7SHWWZRHC5RUIL4PBUW","short_pith_number":"pith:ZAUCVZD7","schema_version":"1.0","canonical_sha256":"c8282ae47f91ed6cc4e2ec6885f1e1a586383b72c3d12786aeb80a3d11b49c2f","source":{"kind":"arxiv","id":"1811.00509","version":1},"attestation_state":"computed","paper":{"title":"Linear statistics and pushed Coulomb gas at the edge of beta random matrices: four paths to large deviations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.dis-nn","math-ph","math.MP","math.PR"],"primary_cat":"cond-mat.stat-mech","authors_text":"Alexandre Krajenbrink, Pierre Le Doussal","submitted_at":"2018-11-01T17:26:55Z","abstract_excerpt":"The Airy$_\\beta$ point process, $a_i \\equiv N^{2/3} (\\lambda_i-2)$, describes the eigenvalues $\\lambda_i$ at the edge of the Gaussian $\\beta$ ensembles of random matrices for large matrix size $N \\to \\infty$. We study the probability distribution function (PDF) of linear statistics ${\\sf L}= \\sum_i t \\varphi(t^{-2/3} a_i)$ for large parameter $t$. We show the large deviation forms $\\mathbb{E}_{{\\rm Airy},\\beta}[\\exp(-{\\sf L})] \\sim \\exp(- t^2 \\Sigma[\\varphi])$ and $P({\\sf L}) \\sim \\exp(- t^2 G(L/t^2))$ for the cumulant generating function and the PDF. We obtain the exact rate function $\\Sigma["},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1811.00509","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2018-11-01T17:26:55Z","cross_cats_sorted":["cond-mat.dis-nn","math-ph","math.MP","math.PR"],"title_canon_sha256":"09554c8fbe76353b474152297446b0687eec6000206cf125d1d0ad0a2f310063","abstract_canon_sha256":"6c46cf69954eafd13df15311ad3884c0b3081e9bf4f1145be9f70940bb364f6b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:50:11.684037Z","signature_b64":"pa3OTf7YnaTysSNsU3qnKddUSG1H/ylCMfpanIiuzMUVDIlLZ+rD6Fk+oIckHhu6++MNL5XPERB5JGumdgj3CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c8282ae47f91ed6cc4e2ec6885f1e1a586383b72c3d12786aeb80a3d11b49c2f","last_reissued_at":"2026-05-17T23:50:11.683422Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:50:11.683422Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Linear statistics and pushed Coulomb gas at the edge of beta random matrices: four paths to large deviations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.dis-nn","math-ph","math.MP","math.PR"],"primary_cat":"cond-mat.stat-mech","authors_text":"Alexandre Krajenbrink, Pierre Le Doussal","submitted_at":"2018-11-01T17:26:55Z","abstract_excerpt":"The Airy$_\\beta$ point process, $a_i \\equiv N^{2/3} (\\lambda_i-2)$, describes the eigenvalues $\\lambda_i$ at the edge of the Gaussian $\\beta$ ensembles of random matrices for large matrix size $N \\to \\infty$. We study the probability distribution function (PDF) of linear statistics ${\\sf L}= \\sum_i t \\varphi(t^{-2/3} a_i)$ for large parameter $t$. We show the large deviation forms $\\mathbb{E}_{{\\rm Airy},\\beta}[\\exp(-{\\sf L})] \\sim \\exp(- t^2 \\Sigma[\\varphi])$ and $P({\\sf L}) \\sim \\exp(- t^2 G(L/t^2))$ for the cumulant generating function and the PDF. We obtain the exact rate function $\\Sigma["},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.00509","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":"1811.00509","created_at":"2026-05-17T23:50:11.683512+00:00"},{"alias_kind":"arxiv_version","alias_value":"1811.00509v1","created_at":"2026-05-17T23:50:11.683512+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.00509","created_at":"2026-05-17T23:50:11.683512+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZAUCVZD7SHWW","created_at":"2026-05-18T12:33:04.347982+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZAUCVZD7SHWWZRHC","created_at":"2026-05-18T12:33:04.347982+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZAUCVZD7","created_at":"2026-05-18T12:33:04.347982+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/ZAUCVZD7SHWWZRHC5RUIL4PBUW","json":"https://pith.science/pith/ZAUCVZD7SHWWZRHC5RUIL4PBUW.json","graph_json":"https://pith.science/api/pith-number/ZAUCVZD7SHWWZRHC5RUIL4PBUW/graph.json","events_json":"https://pith.science/api/pith-number/ZAUCVZD7SHWWZRHC5RUIL4PBUW/events.json","paper":"https://pith.science/paper/ZAUCVZD7"},"agent_actions":{"view_html":"https://pith.science/pith/ZAUCVZD7SHWWZRHC5RUIL4PBUW","download_json":"https://pith.science/pith/ZAUCVZD7SHWWZRHC5RUIL4PBUW.json","view_paper":"https://pith.science/paper/ZAUCVZD7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1811.00509&json=true","fetch_graph":"https://pith.science/api/pith-number/ZAUCVZD7SHWWZRHC5RUIL4PBUW/graph.json","fetch_events":"https://pith.science/api/pith-number/ZAUCVZD7SHWWZRHC5RUIL4PBUW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZAUCVZD7SHWWZRHC5RUIL4PBUW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZAUCVZD7SHWWZRHC5RUIL4PBUW/action/storage_attestation","attest_author":"https://pith.science/pith/ZAUCVZD7SHWWZRHC5RUIL4PBUW/action/author_attestation","sign_citation":"https://pith.science/pith/ZAUCVZD7SHWWZRHC5RUIL4PBUW/action/citation_signature","submit_replication":"https://pith.science/pith/ZAUCVZD7SHWWZRHC5RUIL4PBUW/action/replication_record"}},"created_at":"2026-05-17T23:50:11.683512+00:00","updated_at":"2026-05-17T23:50:11.683512+00:00"}