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
SN - 0022-2488
VL - 51
JO - Journal of Mathematical Physics
JF - Journal of Mathematical Physics
IS - 9
M1 - 093304
ER -