Asymptotic spectra of matrix-valued functions of independent random matrices and free probability

被引：19
|
作者：
Goetze, F. [1 ]
Koesters, H. [1 ]
Tikhomirov, A. [2 ]
机构：
[1] Univ Bielefeld, Fac Math, Bielefeld, Germany
[2] Syktyvkar State Univ, RAS, Dept Math, Komi Sci Ctr,Ural Div, Syktyvkar, Russia
来源：
RANDOM MATRICES-THEORY AND APPLICATIONS | 2015年 / 4卷 / 02期
关键词：
Asymptotic spectral distributions; functions of independent random matrices; free probability; Stieltjes transform; logarithmic potential; SINGULAR-VALUES; CIRCULAR LAW; S-TRANSFORM; PRODUCT; POWERS;
D O I：
10.1142/S2010326315500057
中图分类号：
O4 [物理学];
学科分类号：
0702 ;
摘要：
We investigate the universality of singular value and eigenvalue distributions of matrix-valued functions of independent random matrices and apply these general results in several examples. In particular we determine the limit distribution and prove universality under general conditions for singular value and eigenvalue distributions of products of independent matrices from spherical ensembles.
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页数：85
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