R-transforms for non-Hermitian matrices derive from one scalar function of two variables via spherical integrals and the replica method.
Lidskii’s theorem in the type II case, Geometric methods in operator algebras (Kyoto 1983), H
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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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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.