Characteristic polynomials of non-Hermitian random band matrices
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915544403279872 |
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| author | Shcherbina, Mariya Shcherbina, Tatyana |
| author_facet | Shcherbina, Mariya Shcherbina, Tatyana |
| contents | We consider the asymptotic local behavior of the second correlation functions of the characteristic polynomials of a certain class of Gaussian $N\times N$ non-Hermitian random band matrices with a bandwidth $W$. Given $W,N\to\infty$, we show that this behavior near the point in the bulk of the spectrum exhibits the crossover at $W\sim \sqrt{N}$: it coincides with those for Ginibre ensemble for $W\gg \sqrt{N}$, and factorized as $1\ll W\ll \sqrt{N}$. The result is the first step toward the proof of Anderson's type transition for non-Hermitian random band matrices. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_04255 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Characteristic polynomials of non-Hermitian random band matrices Shcherbina, Mariya Shcherbina, Tatyana Mathematical Physics 60B20 We consider the asymptotic local behavior of the second correlation functions of the characteristic polynomials of a certain class of Gaussian $N\times N$ non-Hermitian random band matrices with a bandwidth $W$. Given $W,N\to\infty$, we show that this behavior near the point in the bulk of the spectrum exhibits the crossover at $W\sim \sqrt{N}$: it coincides with those for Ginibre ensemble for $W\gg \sqrt{N}$, and factorized as $1\ll W\ll \sqrt{N}$. The result is the first step toward the proof of Anderson's type transition for non-Hermitian random band matrices. |
| title | Characteristic polynomials of non-Hermitian random band matrices |
| topic | Mathematical Physics 60B20 |
| url | https://arxiv.org/abs/2510.04255 |