Universal sum and product rules for random matrices
Rogers, T., 2010. Universal sum and product rules for random matrices. Journal of Mathematical Physics, 51 (9), 093304.
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The spectral density of random matrices is studied through a quaternionic generalisation of the Green's function, which precisely describes the mean spectral density of a given matrix under a particular type of random perturbation. Exact and universal expressions are found in the high-dimension limit for the quaternionic Green's functions of random matrices with independent entries when summed or multiplied with deterministic matrices. From these, the limiting spectral density can be accurately predicted.
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