Repeated erfc statistics for deformed GinUEs

Dang-Zheng Liu; Lu Zhang

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arXiv · 2402.14362

Repeated erfc statistics for deformed GinUEs

Dang-Zheng Liu·Lu Zhang

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Abstract

For an additive perturbation of the complex Ginibre ensemble under a deterministic matrix $X_0$, under certain assumption on $X_0$, we observe that there are only two kinds of local statistical patterns at the spectral edge: GinUE statistics and critical statistics, which corresponds to regular or quadratic vanishing spectral points. As a continuation of our previous study on critical statistics "Critical edge statistics for deformed GinUEs"(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 "Phase transition of eigenvalues in deformed Ginibre ensembles"(arXiv: 2204.13171v2).

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Dang-Zheng Liu, Lu Zhang. 2024-02-22. Repeated erfc statistics for deformed GinUEs. https://arxiv.org/abs/2402.14362

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