{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:7V4IW4FEMWSIUHAQTLQAPTKMG2","short_pith_number":"pith:7V4IW4FE","schema_version":"1.0","canonical_sha256":"fd788b70a465a48a1c109ae007cd4c36b3a4719c530110b2a1fc1c9390bb79bc","source":{"kind":"arxiv","id":"2501.08039","version":1},"attestation_state":"computed","paper":{"title":"Exact convergence rate of spectral radius of complex Ginibre to Gumbel distribution","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Xujia Meng, Yutao ma","submitted_at":"2025-01-14T11:43:10Z","abstract_excerpt":"Consider the complex Ginibre ensemble, whose eigenvalues are $(\\lambda_i)_{1\\le i\\le n}$ and the spectral radius $R_n=\\max_{1\\le i\\le n}|\\lambda_i|.$ Set $X_n=\\sqrt{4 \\gamma_{n}}(R_{n}-\\sqrt{n}-\\frac12\\sqrt{\\gamma_{n}})$ and $F_n$ be its distribution function, where $\\gamma_{n}=\\log n-2\\log(\\sqrt{2\\pi}\\log n).$ It was proved in \\cite{Rider 2003} that $F_n$ converges weakly to the Gumbel distribution $\\Lambda.$ We prove in further in this paper that $$\\lim_{n\\to\\infty} \\frac{\\log n}{\\log\\log n}\\, W_1\\left(F_n, \\Lambda\\right)=2$$\n  and the Berry-Esseen bound\n  $$\\lim\\limits_{n\\to \\infty} \\frac{\\"},"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":"2501.08039","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2025-01-14T11:43:10Z","cross_cats_sorted":[],"title_canon_sha256":"9e759218ac0469415a5e396d5b9b3ec0deb2255fdfa2096e8aaa06969d43d100","abstract_canon_sha256":"9fbcbf2ab88b1598cf63c1a8165b65dd1e337c3179f2b241968ad03cd7cf889e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:00:54.699072Z","signature_b64":"WrwCcHPz3YOYOlsXL55VHle5QNSPkbpS4L3sJDUebHHTpqyVM63xrVKBDLyLkQg1YMYzI6iv/7WzEhKFy9h8Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fd788b70a465a48a1c109ae007cd4c36b3a4719c530110b2a1fc1c9390bb79bc","last_reissued_at":"2026-07-05T10:00:54.698491Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:00:54.698491Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Exact convergence rate of spectral radius of complex Ginibre to Gumbel distribution","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Xujia Meng, Yutao ma","submitted_at":"2025-01-14T11:43:10Z","abstract_excerpt":"Consider the complex Ginibre ensemble, whose eigenvalues are $(\\lambda_i)_{1\\le i\\le n}$ and the spectral radius $R_n=\\max_{1\\le i\\le n}|\\lambda_i|.$ Set $X_n=\\sqrt{4 \\gamma_{n}}(R_{n}-\\sqrt{n}-\\frac12\\sqrt{\\gamma_{n}})$ and $F_n$ be its distribution function, where $\\gamma_{n}=\\log n-2\\log(\\sqrt{2\\pi}\\log n).$ It was proved in \\cite{Rider 2003} that $F_n$ converges weakly to the Gumbel distribution $\\Lambda.$ We prove in further in this paper that $$\\lim_{n\\to\\infty} \\frac{\\log n}{\\log\\log n}\\, W_1\\left(F_n, \\Lambda\\right)=2$$\n  and the Berry-Esseen bound\n  $$\\lim\\limits_{n\\to \\infty} \\frac{\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.08039","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2501.08039/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2501.08039","created_at":"2026-07-05T10:00:54.698560+00:00"},{"alias_kind":"arxiv_version","alias_value":"2501.08039v1","created_at":"2026-07-05T10:00:54.698560+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2501.08039","created_at":"2026-07-05T10:00:54.698560+00:00"},{"alias_kind":"pith_short_12","alias_value":"7V4IW4FEMWSI","created_at":"2026-07-05T10:00:54.698560+00:00"},{"alias_kind":"pith_short_16","alias_value":"7V4IW4FEMWSIUHAQ","created_at":"2026-07-05T10:00:54.698560+00:00"},{"alias_kind":"pith_short_8","alias_value":"7V4IW4FE","created_at":"2026-07-05T10:00:54.698560+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2510.07942","citing_title":"Precise convergence rate of spectral radius of product of complex Ginibre","ref_index":28,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/7V4IW4FEMWSIUHAQTLQAPTKMG2","json":"https://pith.science/pith/7V4IW4FEMWSIUHAQTLQAPTKMG2.json","graph_json":"https://pith.science/api/pith-number/7V4IW4FEMWSIUHAQTLQAPTKMG2/graph.json","events_json":"https://pith.science/api/pith-number/7V4IW4FEMWSIUHAQTLQAPTKMG2/events.json","paper":"https://pith.science/paper/7V4IW4FE"},"agent_actions":{"view_html":"https://pith.science/pith/7V4IW4FEMWSIUHAQTLQAPTKMG2","download_json":"https://pith.science/pith/7V4IW4FEMWSIUHAQTLQAPTKMG2.json","view_paper":"https://pith.science/paper/7V4IW4FE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2501.08039&json=true","fetch_graph":"https://pith.science/api/pith-number/7V4IW4FEMWSIUHAQTLQAPTKMG2/graph.json","fetch_events":"https://pith.science/api/pith-number/7V4IW4FEMWSIUHAQTLQAPTKMG2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7V4IW4FEMWSIUHAQTLQAPTKMG2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7V4IW4FEMWSIUHAQTLQAPTKMG2/action/storage_attestation","attest_author":"https://pith.science/pith/7V4IW4FEMWSIUHAQTLQAPTKMG2/action/author_attestation","sign_citation":"https://pith.science/pith/7V4IW4FEMWSIUHAQTLQAPTKMG2/action/citation_signature","submit_replication":"https://pith.science/pith/7V4IW4FEMWSIUHAQTLQAPTKMG2/action/replication_record"}},"created_at":"2026-07-05T10:00:54.698560+00:00","updated_at":"2026-07-05T10:00:54.698560+00:00"}