Bulk behavior of Schur-Hadamard products of symmetric random matrices

被引：3

作者：

Bose, Arup ^{[1
]}

Mukherjee, Soumendu Sundar ^{[2
]}

机构：

[1] Indian Stat Inst, Stat & Math Unit, 203 BT Rd, Kolkata 700108, India

[2] Indian Stat Inst, Kolkata 700108, India

来源：

RANDOM MATRICES-THEORY AND APPLICATIONS | 2014年 / 3卷 / 02期

关键词：

Patterned matrices; Schur-Hadamard product; limiting spectral distribution; Toeplitz; Wigner; Hankel; Circulant matrices; semi-circular law;

D O I：

10.1142/S2010326314500075

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We develop a general method for establishing the existence of the Limiting Spectral Distributions (LSD) of Schur-Hadamard products of independent symmetric patterned random matrices. We apply this method to show that the LSD of Schur-Hadamard products of some common patterned matrices exist and identify the limits. In particular, the Schur-Hadamard product of independent Toeplitz and Hankel matrices has the semicircular LSD. We also prove an invariance theorem that may be used to find the LSD in many examples.

引用

页数：25

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