Universality of the second correlation function of the deformed Ginibre ensemble
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866909670754484224 |
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| author | Afanasiev, Ievgenii Shcherbina, Mariya Shcherbina, Tatyana |
| author_facet | Afanasiev, Ievgenii Shcherbina, Mariya Shcherbina, Tatyana |
| contents | We study the deformed complex Ginibre ensemble $H=A_0+H_0$, where $H_0$ is the complex matrix with iid Gaussian entries, and $A_0$ is some general $n\times n$ matrix (it can be random and in this case it is independent of $H_0$). Assuming rather general assumptions on $A_0$, we prove that the asymptotic local behavior of the second correlation function of the eigenvalues of such matrices in the bulk coincides with that for the pure complex Ginibre ensemble. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2405_00617 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Universality of the second correlation function of the deformed Ginibre ensemble Afanasiev, Ievgenii Shcherbina, Mariya Shcherbina, Tatyana Mathematical Physics 60B20 We study the deformed complex Ginibre ensemble $H=A_0+H_0$, where $H_0$ is the complex matrix with iid Gaussian entries, and $A_0$ is some general $n\times n$ matrix (it can be random and in this case it is independent of $H_0$). Assuming rather general assumptions on $A_0$, we prove that the asymptotic local behavior of the second correlation function of the eigenvalues of such matrices in the bulk coincides with that for the pure complex Ginibre ensemble. |
| title | Universality of the second correlation function of the deformed Ginibre ensemble |
| topic | Mathematical Physics 60B20 |
| url | https://arxiv.org/abs/2405.00617 |