Additive/Multiplicative Free Subordination Property and Limiting Eigenvectors of Spiked Additive Deformations of Wigner Matrices and Spiked Sample Covariance Matrices

被引：20

作者：

Capitaine, M. ^{[1
]}

机构：

[1] CNRS, Inst Math Toulouse, Equipe Stat & Probabilites, F-31062 Toulouse 09, France

来源：

JOURNAL OF THEORETICAL PROBABILITY | 2013年 / 26卷 / 03期

关键词：

Random matrices; Spiked deformations of Wigner matrices; Spiked sample covariance matrices; Eigenvalues; Eigenvectors; Free probability; Subordination property; LARGEST EIGENVALUE; FREE CONVOLUTION; SPECTRAL DISTRIBUTION; CONVERGENCE;

D O I：

10.1007/s10959-012-0416-5

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：

When some eigenvalues of a spiked additive deformation of a Wigner matrix or a spiked multiplicative deformation of a Wishart matrix separate from the bulk, we study how the corresponding eigenvectors project onto those of the perturbation. We point out that the subordination function relative to the free (additive or multiplicative) convolution plays an important part in the asymptotic behavior.

引用

页码：595 / 648

页数：54