Strong convergence of the empirical distribution of eigenvalues of sample covariance matrices with a perturbation matrix |
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Authors: | Guangming Pan |
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Institution: | Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore |
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Abstract: | Let , where is a random symmetric matrix, a random symmetric matrix, and with being independent real random variables. Suppose that , and are independent. It is proved that the empirical spectral distribution of the eigenvalues of random symmetric matrices converges almost surely to a non-random distribution. |
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Keywords: | primary 15A52 secondary 15A90 60E05 |
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