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

  • Bai, Z.D.
  • Miao, Baiqi
  • Jin, Baisuo
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    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 SnWn is established, where Sn is a sample covariance matrix and Wn is Wigner matrix.

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    Article provided by Elsevier in its journal Journal of Multivariate Analysis.

    Volume (Year): 98 (2007)
    Issue (Month): 1 (January)
    Pages: 76-101

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    Handle: RePEc:eee:jmvana:v:98:y:2007:i:1:p:76-101
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    1. Bai, Z. D. & Yin, Y. Q. & Krishnaiah, P. R., 1986. "On limiting spectral distribution of product of two random matrices when the underlying distribution is isotropic," Journal of Multivariate Analysis, Elsevier, vol. 19(1), pages 189-200, June.
    2. Silverstein, J. W., 1995. "Strong Convergence of the Empirical Distribution of Eigenvalues of Large Dimensional Random Matrices," Journal of Multivariate Analysis, Elsevier, vol. 55(2), pages 331-339, November.
    3. Yin, Y. Q. & Bai, Z. D. & Krishnaiah, P. R., 1983. "Limiting behavior of the eigenvalues of a multivariate F matrix," Journal of Multivariate Analysis, Elsevier, vol. 13(4), pages 508-516, December.
    4. Yin, Y. Q. & Krishnaiah, P. R., 1983. "A limit theorem for the eigenvalues of product of two random matrices," Journal of Multivariate Analysis, Elsevier, vol. 13(4), pages 489-507, December.
    5. Yin, Y. Q., 1986. "Limiting spectral distribution for a class of random matrices," Journal of Multivariate Analysis, Elsevier, vol. 20(1), pages 50-68, October.
    6. Silverstein, J. W. & Bai, Z. D., 1995. "On the Empirical Distribution of Eigenvalues of a Class of Large Dimensional Random Matrices," Journal of Multivariate Analysis, Elsevier, vol. 54(2), pages 175-192, August.
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