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In the present paper, we prove that under the assumption of the finite sixth moment for elements of a Wigner matrix, the convergence rate of its empirical spectral distribution to the Wigner semicircular law in probability is $O(n^{-1/2})$ when the dimension $n$ tends to infinity.
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E. P. Wigner · 1955
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Convergence rate of expected spectral distributions of large random matrices. Part I. Wigner matrices
Z. D. Bai · 1993
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Convergence rate of expected spectral distributions of large random matrices. Part II. Sample covariance matrices
Z. D. Bai · 1993
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On the empirical distribution of eigenvalues of a class of largedimensional random matrices
J. W. Silverstein and Z. D. Bai · 1995
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A note on the convergence rate of the spectral distributions of large random matrices
Z. D. Bai, B. Q. Miao, and J. Tsay · 1997
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Convergence rates of the spectral distributions of large Wigner matrices
Z. D. Bai, B. Q. Miao, and J. Tsay · 2002
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Random matrices, Third Edition
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CLT for linear spectral statistics of Wigner matrices
Z. D. Bai, X. Y. Wang, and W. Zhou · 2009
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On the rate of convergence of the expected spectral distribution function of a Wigner matrix to the semi-circular law
A. Tikhomirov · 2009
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An introduction to random matrices
G. W. Anderson, A. Guionnet, and O. Zeitouni · 2010
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Spectral analysis of large dimensional random matrices. Second Edition
Z. D. Bai and J. W. Silverstein · 2010
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On concentration of empirical measures and convergence to the semi-circle law
S. G. Bobkov, F. Götze, and A. N. Tikhomirov · 2010
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