Finite-rank normal perturbations of large rotationally invariant non-Hermitian random matrices produce outlier eigenvalues whose positions and fluctuations, together with the associated eigenvectors, are characterized in a unified framework that includes the Hermitian case.
The single ring theorem.Annals of mathematics, pages 1189–1217
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R-transforms for non-Hermitian matrices derive from one scalar function of two variables via spherical integrals and the replica method.
Spectral boundaries of A + B (A deterministic, B rotationally invariant random non-Hermitian) are given by simple equations depending on the R1 and R2 transforms of B in the large-N limit.
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The eigenvalues and eigenvectors of finite-rank normal perturbations of large rotationally invariant non-Hermitian matrices
Finite-rank normal perturbations of large rotationally invariant non-Hermitian random matrices produce outlier eigenvalues whose positions and fluctuations, together with the associated eigenvectors, are characterized in a unified framework that includes the Hermitian case.
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R-transforms for non-Hermitian matrices: a spherical integral approach
R-transforms for non-Hermitian matrices derive from one scalar function of two variables via spherical integrals and the replica method.
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Spectral boundaries of deterministic matrices deformed by rotationally invariant random non-Hermitian ensembles
Spectral boundaries of A + B (A deterministic, B rotationally invariant random non-Hermitian) are given by simple equations depending on the R1 and R2 transforms of B in the large-N limit.