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arXiv · 0912.2499

Universal sum and product rules for random matrices

Tim Rogers
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Abstract

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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Tim Rogers. 2010-02-18. Universal sum and product rules for random matrices. https://doi.org/10.1063/1.3481569

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