{"paper":{"title":"Optimal $W_1$ and Berry-Esseen bound between the spectral radius of large Chiral non-Hermitian random matrices and Gumbel","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Siyu Wang, Yutao ma","submitted_at":"2025-01-15T08:56:02Z","abstract_excerpt":"Consider the chiral non-Hermitian random matrix ensemble with parameters $n$ and $v$ and the non Hermiticity parameter $\\tau=0$ and let $(\\zeta_i)_{1\\le i\\le n}$ be its $n$ eigenvalues with positive $x$-coordinate. Set $$X_n:=\\sqrt{\\log s_n}\\left(\\frac{2n \\max_{1\\le i\\le n}|\\zeta_i|^2-2\\sqrt{n(n+v)}}{\\sqrt{2n+v}}-a(s_{n})\\right)$$ with $s_n=n(n+v)/(2n+v)$ and $a(s_n)=\\sqrt{\\log s_n}-\\frac{\\log(\\sqrt{2\\pi}\\log s_n)}{\\sqrt{\\log s_n}}.$ It was proved in \\cite{JQ} that $X_n$ converges weakly to the Gumbel distribution $\\Lambda$. In this paper, we give in further that $$\\lim_{n\\to\\infty} \\frac{\\log"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.08661","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2501.08661/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"}