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Universal sum and product rules for random matrices. (English) Zbl 1309.82016

Summary: The spectral density of random matrices is studied through a quaternionic generalization 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.{
©2010 American Institute of Physics}

MSC:

82B31 Stochastic methods applied to problems in equilibrium statistical mechanics
60B20 Random matrices (probabilistic aspects)
15B33 Matrices over special rings (quaternions, finite fields, etc.)
15B52 Random matrices (algebraic aspects)
35J08 Green’s functions for elliptic equations
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References:

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