








Abstract:We study finite-rank normal deformations of rotationally invariant non-Hermitian random matrices. Extending the classical Baik-Ben Arous-Péché (BBP) framework, we characterize the emergence and fluctuations of outlier eigenvalues in models of the form $\mathbf{A} + \mathbf{T}$, where $\mathbf{A}$ is a large rotationally invariant non-Hermitian random matrix and $\mathbf{T}$ is a finite-rank normal perturbation. We also describe the corresponding eigenvector behavior. Our results provide a unified framework encompassing both Hermitian and non-Hermitian settings, thereby generalizing several known cases.
From: Pierre Bousseyroux [view email]
[v1]
Thu, 15 Jan 2026 14:21:54 UTC (32 KB)
[v2]
Thu, 14 May 2026 11:03:26 UTC (32 KB)
[v3]
Tue, 1 Sep 2026 13:17:25 UTC (32 KB)
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