Tim Rogers
Published 2009-12-13, updated 2010-02-18Version 2
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.
Journal: J. Math. Phys. 51, 093304 (2010)
Application of the $τ$-function theory of Painlevé equations to random matrices: \PVI, the JUE, CyUE, cJUE and scaled limits
Integrability, Random Matrices and Painlevé Transcendents
Universality at the edge of the spectrum for unitary, orthogonal and symplectic ensembles of random matrices
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