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Eigenvalue distributions of random unitary matrices
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  • Published: June 2002

Eigenvalue distributions of random unitary matrices

  • K. Wieand1 

Probability Theory and Related Fields volume 123, pages 202–224 (2002)Cite this article

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  • 32 Citations

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Abstract.

 Let U be an n × n random matrix chosen from Haar measure on the unitary group. For a fixed arc of the unit circle, let X be the number of eigenvalues of M which lie in the specified arc. We study this random variable as the dimension n grows, using the connection between Toeplitz matrices and random unitary matrices, and show that (X -E [X])/(\Var (X))1/2 is asymptotically normally distributed. In addition, we show that for several fixed arcs I 1 , ..., I m , the corresponding random variables are jointly normal in the large n limit.

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Authors and Affiliations

  1. Department of Health Studies, University of Chicago, 5841 S. Maryland Ave., MC 2007, Chicago, IL 60637, USA. e-mail: klwieand@post.harvard.edu, , , , , , US

    K. Wieand

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  1. K. Wieand
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Received: 15 November 2000 / Revised version: 27 September 2001 / Published online: 17 May 2002

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Wieand, K. Eigenvalue distributions of random unitary matrices. Probab. Theory Relat. Fields 123, 202–224 (2002). https://doi.org/10.1007/s004400100186

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  • Issue Date: June 2002

  • DOI: https://doi.org/10.1007/s004400100186

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Keywords

  • Unit Circle
  • Random Matrix
  • Unitary Group
  • Unitary Matrice
  • Eigenvalue Distribution
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