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arXiv · 2404.17512

On the spectral edge of non-Hermitian random matrices

Andrew Campbell·Giorgio Cipolloni·László Erdős·Hong Chang Ji
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Abstract

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.

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Andrew Campbell, Giorgio Cipolloni, László Erdős, Hong Chang Ji. 2024-04-26. On the spectral edge of non-Hermitian random matrices. https://arxiv.org/abs/2404.17512

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