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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2402.14362 |
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| _version_ | 1866909116712091648 |
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| author | Liu, Dang-Zheng Zhang, Lu |
| author_facet | Liu, Dang-Zheng Zhang, Lu |
| contents | 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). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_14362 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Repeated erfc statistics for deformed GinUEs Liu, Dang-Zheng Zhang, Lu Probability 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). |
| title | Repeated erfc statistics for deformed GinUEs |
| topic | Probability |
| url | https://arxiv.org/abs/2402.14362 |