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On Concentration of Empirical Measures and Convergence to the Semi-circle Law

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Abstract

Concentration properties of the general empirical distribution functions and the rate of convergence of spectral empirical distributions to the semi-circle law in the case of symmetric high-dimensional random matrices are studied under Poincaré-type inequalities.

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Authors and Affiliations

  1. School of Mathematics, University of Minnesota, Minneapolis, USA

    S. G. Bobkov

  2. Faculty of Mathematics, University of Bielefeld, Bielefeld, Germany

    F. Götze

  3. Department of Mathematics of Komi Research Center of RAS, Syktyvkar, Russia

    A. N. Tikhomirov

Authors
  1. S. G. Bobkov
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  2. F. Götze
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  3. A. N. Tikhomirov
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Corresponding author

Correspondence to S. G. Bobkov.

Additional information

Research partially supported by NSF grant DMS-0706866, SFB 701, RFBR grant N07-01-00583-a, and RF grant of the leading scientific schools NSh-638.2008.1.

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Bobkov, S.G., Götze, F. & Tikhomirov, A.N. On Concentration of Empirical Measures and Convergence to the Semi-circle Law. J Theor Probab 23, 792–823 (2010). https://doi.org/10.1007/s10959-010-0286-7

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  • DOI: https://doi.org/10.1007/s10959-010-0286-7

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