Universal sum and product rules for random matrices

Details Universal sum and product rules for random matrices Universal sum and product rules for random matrices

2009-12-13

arxiv.org/abs/0912.2499v2

J. Math. Phys. 51, 093304 (2010)

Physics

Mathematical Physics

Scientific paper

10.1063/1.3481569

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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