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Rate of convergence to the semi-circular law
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  • Published: 15 July 2003

Rate of convergence to the semi-circular law

  • F. Götze1 &
  • A. Tikhomirov2 

Probability Theory and Related Fields volume 127, pages 228–276 (2003)Cite this article

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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Author information

Authors and Affiliations

  1. Fakultät für Mathematik, Universität Bielefeld, 33501, Bielefeld 1, Germany

    F. Götze

  2. Faculty of Mathematics, Syktyvkar University, Oktjabrskyi prospekt 55, 167001, Syktyvkar, Russia

    A. Tikhomirov

Authors
  1. F. Götze
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  2. A. Tikhomirov
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Corresponding author

Correspondence to F. Götze.

Additional information

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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Cite this article

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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  • Received: 27 July 2001

  • Revised: 07 February 2003

  • Published: 15 July 2003

  • Issue Date: October 2003

  • DOI: https://doi.org/10.1007/s00440-003-0285-z

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Key words or phrases:

  • Independent random variables
  • Spectral distribution
  • Random matrix
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