On limit theorem for the eigenvalues of product of two random matrices

Authors:
Z. D. Bai;Baiqi Miao;Baisuo Jin
Affiliations:
School of Mathematics and Statistics, KLASMOE, Northeast Normal University, Changchun, China and Department of Statistics and Applied Probability, National University of Singapore, Singapore, Sing ...;Department of Statistics and Finance, University Science and Technology of China, Hefei, Anhui, China;Department of Statistics and Finance, University Science and Technology of China, Hefei, Anhui, China
Venue:
Journal of Multivariate Analysis
Year:
2007

Citing 4
Cited 2

Limiting spectral distribution for a class of random matrices

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On limiting spectral distribution of product of two random matrices when the underlying distribution is isotropic

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On the empirical distribution of eigenvalues of a class of large dimensional random matrices

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Strong convergence of the empirical distribution of eigenvalues of large dimensional random matrices

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Limiting spectral distribution of large-dimensional sample covariance matrices generated by VARMA

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Strong convergence of the empirical distribution of eigenvalues of sample covariance matrices with a perturbation matrix

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Abstract

The existence of limiting spectral distribution (LSD) of the product of two random matrices is proved. One of the random matrices is a sample covariance matrix and the other is an arbitrary Hermitian matrix. Specially, the density function of LSD of Sn Wn is established, where Sn is a sample covariance matrix and Wn is Wigner matrix.