TY - JOUR

T1 - Universal sum and product rules for random matrices

AU - Rogers, Tim

PY - 2010/9

Y1 - 2010/9

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=78049429654&partnerID=8YFLogxK

UR - http://arxiv.org/abs/0912.2499

UR - http://dx.doi.org/10.1063/1.3481569

U2 - 10.1063/1.3481569

DO - 10.1063/1.3481569

M3 - Article

VL - 51

JO - Journal of Mathematical Physics

JF - Journal of Mathematical Physics

SN - 0022-2488

IS - 9

M1 - 093304

ER -