Abstract.
A stochastic bound of order O P (n −1/2) for the Kolmogorov distance between the spectral distribution function of an n×n matrix from Wigner ensemble and the distribution function of the semi-circular law is obtained. The result holds assuming that the twelfth moment of the entries of the matrix is uniformly bounded.
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Research supported by the DFG-Forschergruppe FOR 399/1-1 ``Spektrale Analyse, Asymptotische Verteilungen und Stochastische Dynamiken''.
Research supported by the DFG-Forschergruppe FOR 399/1-1 ``Spektrale Analyse, Asymptotische Verteilungen und Stochastische Dynamiken''.
Partially supported by Russian Foundation for Fundamental Research Grants NN02-01-00233, 00-15-96019. Partially supported by INTAS N99-01317, DFG-RFBR N99-01-04027.
Mathematics Subject Classification (2000): 60F05
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Götze, F., Tikhomirov, A. Rate of convergence to the semi-circular law. Probab. Theory Relat. Fields 127, 228–276 (2003). https://doi.org/10.1007/s00440-003-0285-z
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DOI: https://doi.org/10.1007/s00440-003-0285-z