On the spectral edge of non-Hermitian random matrices

2024/04/26 by Andrew I. Campbell, Giorgio Cipolloni, Campbell, Andrew +5 · 2 citations
Computer Science · Mathematics · #15B52 #60B20 #FOS: Mathematics #Matrix Theory and Algorithms #Probability (math.PR) #Random Matrices and Applications #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2404.17512

openalex publication_date 2024/04/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 Spec(A+X) is deterministic.

Cited by

• A direct approach to soft and hard edge universality for random normal matrices
• Optimal Delocalization for Non--Hermitian Eigenvectors

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