The eigenvalues of i.i.d. matrices are hyperuniform
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866908849554849792 |
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| author | Cipolloni, Giorgio Erdős, László Kolupaiev, Oleksii |
| author_facet | Cipolloni, Giorgio Erdős, László Kolupaiev, Oleksii |
| contents | We prove that the point process of the eigenvalues of real or complex non-Hermitian matrices $X$ with independent, identically distributed entries is hyperuniform: the variance of the number of eigenvalues in a subdomain $Ω$ of the spectrum is much smaller than the volume of $Ω$. Our main technical novelty is a very precise computation of the covariance between the resolvents of the Hermitization of $X-z_1, X-z_2$, for two distinct complex parameters $z_1,z_2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_17628 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The eigenvalues of i.i.d. matrices are hyperuniform Cipolloni, Giorgio Erdős, László Kolupaiev, Oleksii Probability 60B20, 82C10 We prove that the point process of the eigenvalues of real or complex non-Hermitian matrices $X$ with independent, identically distributed entries is hyperuniform: the variance of the number of eigenvalues in a subdomain $Ω$ of the spectrum is much smaller than the volume of $Ω$. Our main technical novelty is a very precise computation of the covariance between the resolvents of the Hermitization of $X-z_1, X-z_2$, for two distinct complex parameters $z_1,z_2$. |
| title | The eigenvalues of i.i.d. matrices are hyperuniform |
| topic | Probability 60B20, 82C10 |
| url | https://arxiv.org/abs/2602.17628 |