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Concentration and convergence rates for spectral measures of random matrices
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  • Published: 23 March 2012

Concentration and convergence rates for spectral measures of random matrices

  • Elizabeth S. Meckes1 &
  • Mark W. Meckes1 

Probability Theory and Related Fields volume 156, pages 145–164 (2013)Cite this article

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Abstract

The topic of this paper is the typical behavior of the spectral measures of large random matrices drawn from several ensembles of interest, including in particular matrices drawn from Haar measure on the classical Lie groups, random compressions of random Hermitian matrices, and the so-called random sum of two independent random matrices. In each case, we estimate the expected Wasserstein distance from the empirical spectral measure to a deterministic reference measure, and prove a concentration result for that distance. As a consequence we obtain almost sure convergence of the empirical spectral measures in all cases.

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Authors and Affiliations

  1. Department of Mathematics, Case Western Reserve University, 10900 Euclid Ave., Cleveland, OH, 44106, USA

    Elizabeth S. Meckes & Mark W. Meckes

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  1. Elizabeth S. Meckes
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  2. Mark W. Meckes
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Correspondence to Elizabeth S. Meckes.

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Meckes, E.S., Meckes, M.W. Concentration and convergence rates for spectral measures of random matrices. Probab. Theory Relat. Fields 156, 145–164 (2013). https://doi.org/10.1007/s00440-012-0423-6

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  • Received: 27 September 2011

  • Revised: 28 February 2012

  • Accepted: 01 March 2012

  • Published: 23 March 2012

  • Issue Date: June 2013

  • DOI: https://doi.org/10.1007/s00440-012-0423-6

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Mathematics Subject Classification

  • Primary 60B20
  • Secondary 22E30
  • 60B12
  • 60E15
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