Joint convergence of several copies of different patterned random matrices

被引：2

作者：

Basu, Riddhipratim ^{[1
]}

Bose, Arup ^{[2
]}

Ganguly, Shirshendu ^{[3
]}

Hazra, Rajat Subhra ^{[4
]}

机构：

[1] Univ Calif Berkeley, Dept Stat, Berkeley, CA 94720 USA

[2] Indian Stat Inst, Stat & Math Unit, Kolkata, India

[3] Univ Washington, Dept Math, Seattle, WA 98195 USA

[4] Univ Zurich, Inst Math, CH-8001 Zurich, Switzerland

来源：

ELECTRONIC JOURNAL OF PROBABILITY | 2012年 / 17卷

关键词：

Random matrices; free probability; joint convergence; patterned matrices; Toeplitz matrix; Hankel matrix; Reverse Circulant matrix; Symmetric Circulant matrix; Wigner matrix; ASYMPTOTIC FREENESS; LARGEST EIGENVALUE; FREE CONVOLUTION; WIGNER; MOMENTS; DEFORMATIONS; UNITARY; REAL; LAWS;

D O I：

10.1214/EJP.v17-1970

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

We study the joint convergence of independent copies of several patterned matrices in the non-commutative probability setup. In particular, joint convergence holds for the well known Wigner, Toeplitz, Hankel, Reverse Circulant and Symmetric Circulant matrices. We also study some properties of the limits. In particular, we show that copies of Wigner becomes asymptotically free with copies of any of the above other matrices.

引用

页码：1 / 33

页数：33

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