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arXiv · 2409.17030

Non-Hermitian spectral universality at critical points

Giorgio Cipolloni·László Erdős·Hong Chang Ji
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Abstract

For general large non-Hermitian random matrices $X$ and deterministic normal deformations $A$, we prove that the local eigenvalue statistics of $A+X$ close to the critical edge points of its spectrum are universal. This concludes the proof of the third and last remaining typical universality class for non-Hermitian random matrices, after bulk and sharp edge universalities have been established in recent years.

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Giorgio Cipolloni, László Erdős, Hong Chang Ji. 2024-09-25. Non-Hermitian spectral universality at critical points. https://doi.org/10.1007/s00440-025-01384-7

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