Characteristic polynomials of non-Hermitian random band matrices near the threshold
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866911599270297600 |
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| author | Shcherbina, Mariya Shcherbina, Tatyana |
| author_facet | Shcherbina, Mariya Shcherbina, Tatyana |
| contents | The paper arXiv:2510.04255 shows that the asymptotic behavior of the second correlation function of characteristic polynomials of the $N\times N$ non-Hermitian random band matrices with a bandwidth $W$ exhibits the transition at $W\sim \sqrt{N}$, as $W,N\to \infty$: it coincides with those for Ginibre ensemble for $W\gg \sqrt{N}$, and factorized as $1\ll W\ll \sqrt{N}$. In this work we extend the techniques of arXiv:2510.04255 to study the critical regime when the bandwidth $W$ is proportional to the threshold $\sqrt{N}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_15355 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Characteristic polynomials of non-Hermitian random band matrices near the threshold Shcherbina, Mariya Shcherbina, Tatyana Mathematical Physics Probability The paper arXiv:2510.04255 shows that the asymptotic behavior of the second correlation function of characteristic polynomials of the $N\times N$ non-Hermitian random band matrices with a bandwidth $W$ exhibits the transition at $W\sim \sqrt{N}$, as $W,N\to \infty$: it coincides with those for Ginibre ensemble for $W\gg \sqrt{N}$, and factorized as $1\ll W\ll \sqrt{N}$. In this work we extend the techniques of arXiv:2510.04255 to study the critical regime when the bandwidth $W$ is proportional to the threshold $\sqrt{N}$. |
| title | Characteristic polynomials of non-Hermitian random band matrices near the threshold |
| topic | Mathematical Physics Probability |
| url | https://arxiv.org/abs/2604.15355 |