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The rate of convergence for spectra of GUE and LUE matrix ensembles

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Central European Journal of Mathematics

Abstract

We obtain optimal bounds of order O(n −1) for the rate of convergence to the semicircle law and to the Marchenko-Pastur law for the expected spectral distribution functions of random matrices from the GUE and LUE, respectively.

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Author information

Authors and Affiliations

  1. Faculty of Mathematics, University of Bielefeld, Germany

    Friedrich Götze

  2. Faculty of Mathematics, Syktyvkar State University, Syktyvkar, Russia

    Alexander Tikhomirov

  3. Department of Mathematics, IMM of the Ural Branch RAS, Syktyvkar, Russia

    Alexander Tikhomirov

Authors
  1. Friedrich Götze
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  2. Alexander Tikhomirov
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Additional information

Research supported by the DFG-Forschergruppe FOR 399/1. Partially supported by INTAS grant N 03-51-5018, by RFBR grant N 02-01-00233, and by RFBR-DFG grant N 04-01-04000.

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Götze, F., Tikhomirov, A. The rate of convergence for spectra of GUE and LUE matrix ensembles. centr.eur.j.math. 3, 666–704 (2005). https://doi.org/10.2478/BF02475626

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  • DOI: https://doi.org/10.2478/BF02475626

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