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arXiv · 2602.17628

The eigenvalues of i.i.d. matrices are hyperuniform

Giorgio Cipolloni·László Erdős·Oleksii Kolupaiev
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Abstract

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 $\Omega$ of the spectrum is much smaller than the volume of $\Omega$. 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 $z_1,z_2$.

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Giorgio Cipolloni, László Erdős, Oleksii Kolupaiev. 2026-02-19. The eigenvalues of i.i.d. matrices are hyperuniform. https://arxiv.org/abs/2602.17628

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