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

Journal of Multivariate Analysis

Volumn 98, Issue 1, 2007, Pages 76-101

  Bai, Z D ^a,b   Miao, Baiqi ^c   Jin, Baisuo ^c  

^a NORTHEAST NORMAL UNIVERSITY   (China)

^b NATIONAL UNIVERSITY OF SINGAPORE   (Singapore)

^c UNIVERSITY OF SCIENCE AND TECHNOLOGY OF CHINA   (China)

Author keywords

Large dimensional random matrices; Limiting spectral distribution; Product of random matrices

Indexed keywords

EID: 33750020003     PISSN: 0047259X     EISSN: 10957243     Source Type: Journal    
DOI: 10.1016/j.jmva.2006.06.001     Document Type: Article

References (14)

1. Bai Z.D. Methodologies in spectral analysis of large dimensional random matrices, a review. Statist. Sinica 9 (1999) 611-677
2. Bai Z.D., and Yin Y.Q. Limiting behavior of the norm of products of random matrices and two problems of Geman-Hwang. Probab. Theory Related Fields 73 (1986) 555-569
3. Bai Z.D., Yin Y.Q., and Krishnaiah P.K. On limiting spectral distribution of product of two random matrices when the underlying distribution is isotropic. J. Multivariate Anal. 19 (1986) 189-200
4. Bai Z.D., Yin Y.Q., and Krishnaiah P.K. On the limiting empirical distribution function of the eigenvalues of a multivariate F-matrix. Probab. Theory Appl. 32 (1987) 490-500
5. R.M. Dudley, An Extended Wichura Theorem, Definitions of Donsker Classes, and Weighted Empirical Distributions, Springer Lecture Notes in Mathematics, vol. 1153, 141C178, Springer, New York, 1985.
6. Feller W. Introduction to Probability Theory and its Applications vol. 2 (1970), Wiley, New York
7. Geman S. The spectral radius of large random matrices. Ann. Probab. 14 4 (1986) 1318-1328
8. Silverstein J.W. The limiting eigenvalue distribution of a multivariate F matrix. SIAM J. Math. Anal. 16 (1985) 641-646
9. Silverstein J.W. Strong convergence of the empirical distribution of eigenvalues of large dimensional random matrices. J. Multivariate Anal. 5 (1995) 331-339
10. Silverstein W.J., and Bai Z.D. On the empirical distribution of eigenvalues of a class of large dimensional random matrices. J. Multivariate Anal. 54 (1995) 175-192
11. Wachter K.W. The limiting empirical measure of multiple discriminant ratios. Ann. Statist. 8 (1980) 937-957
12. Yin Y.Q. Limiting spectral distribution for a class of random matrices. J. Multivariate Anal. 20 (1986) 50-68
13. Yin Y.Q., Bai Z.D., and Krishnaiah P.R. Limiting behavior of the eigenvalues of a multivariate F matrix. J. Multivariate Anal. 13 (1983) 508-516
14. Yin Y.Q., and Krishnaiah P.R. A limit theorem for the eigenvalues of product of two random matrices. J. Multivariate Anal. 13 (1983) 489-507