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<p>For an additive perturbation of the complex Ginibre ensemble under a deterministic matrix <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(X_0\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>X</mi> <mn>0</mn> </msub> </math></EquationSource> </InlineEquation>, under certain assumption on <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(X_0\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>X</mi> <mn>0</mn> </msub> </math></EquationSource> </InlineEquation>, we observe that there are only two kinds of local statistical patterns at the spectral edge: GinUE statistics and critical statistics, which, respectively, correspond to regular and quadratic vanishing spectral points. As a continuation of our previous study on critical statistics (Liu and Zhang in Critical edge statistics for deformed GinUEs. Preprint <a href="http://arxiv.org/abs/2311.13227">arXiv: 2311.13227</a>), in this paper we establish the local statistics of GinUE type at the regular spectral edge, which is characterized by a repeated erfc integral found in Liu and Zhang (Probab Theory Relat Fields. <a href="https://doi.org/10.1007/s00440-024-01318-9">https://doi.org/10.1007/s00440-024-01318-9</a>).</p>

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Repeated Erfc Statistics for Deformed GinUEs

  • 期刊论文

  • 发表日期：

    2025年3月31日

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  • Dang-Zheng Liu,
  • Lu Zhang

摘要

For an additive perturbation of the complex Ginibre ensemble under a deterministic matrix \(X_0\) X 0 , under certain assumption on \(X_0\) X 0 , we observe that there are only two kinds of local statistical patterns at the spectral edge: GinUE statistics and critical statistics, which, respectively, correspond to regular and quadratic vanishing spectral points. As a continuation of our previous study on critical statistics (Liu and Zhang in Critical edge statistics for deformed GinUEs. Preprint arXiv: 2311.13227), in this paper we establish the local statistics of GinUE type at the regular spectral edge, which is characterized by a repeated erfc integral found in Liu and Zhang (Probab Theory Relat Fields. https://doi.org/10.1007/s00440-024-01318-9).