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.
Campbell, A., Cipolloni, G., Erdős, L., Ji, H.c. (2025). On the spectral edge of non-Hermitian random matrices. ANNALS OF PROBABILITY, 53(6), 2256-2308 [10.1214/25-AOP1761].
On the spectral edge of non-Hermitian random matrices
Cipolloni, Giorgio;
2025-01-01
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.| File | Dimensione | Formato | |
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