R-transforms for non-Hermitian matrices derive from one scalar function of two variables via spherical integrals and the replica method.
Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras.Journal of Functional Analysis, 176(2):331–367
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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.