{
  "annotation_id": "f1e58bfe-a642-44f2-9e20-80735d24f685",
  "date_created": "2026-02-17T05:53:20.214000Z",
  "date_modified": "2026-02-17T05:53:20.214000Z",
  "file_hash": "bdc17b18aef168094354a0fec992f60f2c74f9414a17317ea051912a659fa4e2",
  "private": false,
  "record": {
    "abstract": "This paper provides a quantitative analysis of the rightmost eigenvalue for a chiral non-Hermitian random Dirac matrix in the maximally non-Hermitian regime ($\\tau=0$). Let $(\\sigma_i)_{1\\le i\\le n}$ be the eigenvalues with positive real part. We define the normalization constants \\[ s_n = \\frac{4n(n+v)}{2n+v}, \\qquad \\gamma_n = \\frac{1}{2}\\log s_n - \\frac{5}{4}\\log(\\log s_n) - \\log\\bigl(2^{1/4}\\pi\\bigr), \\] and the centered and scaled variable \\[ X_n = \\sqrt{2s_n\\log s_n}\\,\\bigl(\\bigl(\\tfrac{n}{n+v}\\bigr)^{1/4}\\,\\max_{1\\le i\\le n}\\Re\\sigma_i \\;-\\; 1 \\;-\\; \\frac{\\gamma_n}{\\sqrt{2s_n\\log s_n}}\\bigr). \\] Our main result is the following sharp Berry--Esseen bound for the convergence of $X_n$ to the Gumbel distribution: \\[ \\sup_{x \\in \\mathbb{R}} \\bigl|\\mathbb{P}(X_n \\le x) - e^{-e^{-x}}\\bigr| = \\frac{25 (\\log\\log s_n)^2}{16 e \\,\\log s_n}\\,\\bigl(1 + o(1)\\bigr), \\] which holds as $n \\to \\infty$ for an arbitrary parameter $v \\ge 0$ (which may depend on $n$). As a byproduct of our analysis, we also obtain precise large- and moderate-deviation principles for the scaled rightmost eigenvalue $\\bigl(\\frac{n}{n+v}\\bigr)^{1/4} \\max_{1\\le i\\le n}\\Re\\sigma_i$, characterizing its rate of convergence to the value $1$.",
    "arxiv_id": "2601.09204",
    "authors": [
      "Yutao Ma",
      "Xujia Meng"
    ],
    "categories": [
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "title": "Deviation probabilities and Sharp Berry-Esseen bound for rightmost eigenvalue of large non-Hermitian chiral random matrices",
    "url": "https://arxiv.org/abs/2601.09204",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "452ac6ec-5e7a-487f-9147-a8b53d1607d8",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}