{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:D4GV7YNJPRR4QKNEBFKGPXTJL5","short_pith_number":"pith:D4GV7YNJ","schema_version":"1.0","canonical_sha256":"1f0d5fe1a97c63c829a4095467de695f7471d8179b4398e94402cb80da4d1b80","source":{"kind":"arxiv","id":"1210.5400","version":1},"attestation_state":"computed","paper":{"title":"Large deviations of the top eigenvalue of large Cauchy random matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"cond-mat.stat-mech","authors_text":"Dario Villamaina, Gregory Schehr, Pierpaolo Vivo, Satya N. Majumdar","submitted_at":"2012-10-19T12:32:18Z","abstract_excerpt":"We compute analytically the probability density function (pdf) of the largest eigenvalue $\\lambda_{\\max}$ in rotationally invariant Cauchy ensembles of $N\\times N$ matrices. We consider unitary ($\\beta = 2$), orthogonal ($\\beta =1$) and symplectic ($\\beta=4$) ensembles of such heavy-tailed random matrices. We show that a central non-Gaussian regime for $\\lambda_{\\max} \\sim \\mathcal{O}(N)$ is flanked by large deviation tails on both sides which we compute here exactly for any value of $\\beta$. By matching these tails with the central regime, we obtain the exact leading asymptotic behaviors of t"},"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":"1210.5400","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2012-10-19T12:32:18Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"7f9ddad5462500a12204d96c0c0973ff144d373336950718b421b6bf6eb0548a","abstract_canon_sha256":"b29ba4500c91b761c399fcc481430337b95e4f3c51dd2aa3437af7a3be8b207e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:35:25.320862Z","signature_b64":"T0uOzwbu90zceO7btG5bUMtM0hzYJkO69K42eUqnLH6B1LdFIb0vjKoyOxs9P7XOeRMdwFY89b2b4Idy3gOHAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1f0d5fe1a97c63c829a4095467de695f7471d8179b4398e94402cb80da4d1b80","last_reissued_at":"2026-05-18T03:35:25.320156Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:35:25.320156Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Large deviations of the top eigenvalue of large Cauchy random matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"cond-mat.stat-mech","authors_text":"Dario Villamaina, Gregory Schehr, Pierpaolo Vivo, Satya N. Majumdar","submitted_at":"2012-10-19T12:32:18Z","abstract_excerpt":"We compute analytically the probability density function (pdf) of the largest eigenvalue $\\lambda_{\\max}$ in rotationally invariant Cauchy ensembles of $N\\times N$ matrices. We consider unitary ($\\beta = 2$), orthogonal ($\\beta =1$) and symplectic ($\\beta=4$) ensembles of such heavy-tailed random matrices. We show that a central non-Gaussian regime for $\\lambda_{\\max} \\sim \\mathcal{O}(N)$ is flanked by large deviation tails on both sides which we compute here exactly for any value of $\\beta$. By matching these tails with the central regime, we obtain the exact leading asymptotic behaviors of t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.5400","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":"1210.5400","created_at":"2026-05-18T03:35:25.320269+00:00"},{"alias_kind":"arxiv_version","alias_value":"1210.5400v1","created_at":"2026-05-18T03:35:25.320269+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.5400","created_at":"2026-05-18T03:35:25.320269+00:00"},{"alias_kind":"pith_short_12","alias_value":"D4GV7YNJPRR4","created_at":"2026-05-18T12:27:01.376967+00:00"},{"alias_kind":"pith_short_16","alias_value":"D4GV7YNJPRR4QKNE","created_at":"2026-05-18T12:27:01.376967+00:00"},{"alias_kind":"pith_short_8","alias_value":"D4GV7YNJ","created_at":"2026-05-18T12:27:01.376967+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/D4GV7YNJPRR4QKNEBFKGPXTJL5","json":"https://pith.science/pith/D4GV7YNJPRR4QKNEBFKGPXTJL5.json","graph_json":"https://pith.science/api/pith-number/D4GV7YNJPRR4QKNEBFKGPXTJL5/graph.json","events_json":"https://pith.science/api/pith-number/D4GV7YNJPRR4QKNEBFKGPXTJL5/events.json","paper":"https://pith.science/paper/D4GV7YNJ"},"agent_actions":{"view_html":"https://pith.science/pith/D4GV7YNJPRR4QKNEBFKGPXTJL5","download_json":"https://pith.science/pith/D4GV7YNJPRR4QKNEBFKGPXTJL5.json","view_paper":"https://pith.science/paper/D4GV7YNJ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1210.5400&json=true","fetch_graph":"https://pith.science/api/pith-number/D4GV7YNJPRR4QKNEBFKGPXTJL5/graph.json","fetch_events":"https://pith.science/api/pith-number/D4GV7YNJPRR4QKNEBFKGPXTJL5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/D4GV7YNJPRR4QKNEBFKGPXTJL5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/D4GV7YNJPRR4QKNEBFKGPXTJL5/action/storage_attestation","attest_author":"https://pith.science/pith/D4GV7YNJPRR4QKNEBFKGPXTJL5/action/author_attestation","sign_citation":"https://pith.science/pith/D4GV7YNJPRR4QKNEBFKGPXTJL5/action/citation_signature","submit_replication":"https://pith.science/pith/D4GV7YNJPRR4QKNEBFKGPXTJL5/action/replication_record"}},"created_at":"2026-05-18T03:35:25.320269+00:00","updated_at":"2026-05-18T03:35:25.320269+00:00"}