On the spectral edge of non-Hermitian random matrices
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866916838753959936 |
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| author | Campbell, Andrew Cipolloni, Giorgio Erdős, László Ji, Hong Chang |
| author_facet | Campbell, Andrew Cipolloni, Giorgio Erdős, László Ji, Hong Chang |
| contents | For general non-Hermitian random matrices $X$ and deterministic deformation matrices $A$, we prove that the local eigenvalue statistics of $A+X$ close to the typical edge points of its spectrum are universal. Furthermore, we show that under natural assumptions on $A$ the spectrum of $A+X$ does not have outliers at a distance larger than the natural fluctuation scale of the eigenvalues. As a consequence, the number of eigenvalues in each component of $\mathrm{Spec}(A+X)$ is deterministic. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_17512 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the spectral edge of non-Hermitian random matrices Campbell, Andrew Cipolloni, Giorgio Erdős, László Ji, Hong Chang Probability 15B52, 60B20 For general non-Hermitian random matrices $X$ and deterministic deformation matrices $A$, we prove that the local eigenvalue statistics of $A+X$ close to the typical edge points of its spectrum are universal. Furthermore, we show that under natural assumptions on $A$ the spectrum of $A+X$ does not have outliers at a distance larger than the natural fluctuation scale of the eigenvalues. As a consequence, the number of eigenvalues in each component of $\mathrm{Spec}(A+X)$ is deterministic. |
| title | On the spectral edge of non-Hermitian random matrices |
| topic | Probability 15B52, 60B20 |
| url | https://arxiv.org/abs/2404.17512 |