On the asymptotic distribution of block-modified random matrices

被引：15

作者：

Arizmendi, Octavio ^{[1
]}

Nechita, Ion ^{[2
,3
]}

Vargas, Carlos ^{[4
]}

机构：

[1] CIMAT, Dept Probabil & Stat, Guanajuato, Mexico

[2] Tech Univ Munich, Zentrum Math, M5,Boltzmannstr 3, D-85748 Garching, Germany

[3] Univ Toulouse, UPS, CNRS, Phys Theor Lab,IRSAMC, F-31062 Toulouse, France

[4] Graz Univ Technol, Dept Math Struct Theory, Steyrergasse 30-3, A-8010 Graz, Austria

来源：

JOURNAL OF MATHEMATICAL PHYSICS | 2016年 / 57卷 / 01期

基金：

奥地利科学基金会;

关键词：

REDUCTION CRITERION;

D O I：

10.1063/1.4936925

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We study random matrices acting on tensor product spaces which have been transformed by a linear block operation. Using operator-valued free probability theory, under some mild assumptions on the linear map acting on the blocks, we compute the asymptotic eigenvalue distribution of the modified matrices in terms of the initial asymptotic distribution. Moreover, using recent results on operator-valued subordination, we present an algorithm that computes, numerically but in full generality, the limiting eigenvalue distribution of the modified matrices. Our analytical results cover many cases of interest in quantum information theory: we unify some known results and we obtain new distributions and various generalizations. (C) 2015 AIP Publishing LLC.

引用

页数：25

共 31 条

[1]

Anderson Greg W, 2010, INTRO RANDOM MATRICE

[2]

[Anonymous], 2006, LECT COMBINATORICS F, DOI DOI 10.1017/CBO9780511735127

[3] PARTIAL TRANSPOSITION OF RANDOM STATES AND NON-CENTERED SEMICIRCULAR DISTRIBUTIONS [J].