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Large deviation for the empirical eigenvalue density of truncated Haar unitary matrices
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  • Published: 06 June 2005

Large deviation for the empirical eigenvalue density of truncated Haar unitary matrices

  • Dénes Petz1 &
  • Júlia Réffy1 

Probability Theory and Related Fields volume 133, pages 175–189 (2005)Cite this article

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Abstract

Let U m be an m×m Haar unitary matrix and U[ m,n ] be its n×n truncation. In this paper the large deviation is proven for the empirical eigenvalue density of U[ m,n ] as m/n→λ and n→∞. The rate function and the limit distribution are given explicitly. U[ m,n ] is the random matrix model of quq, where u is a Haar unitary in a finite von Neumann algebra, q is a certain projection and they are free. The limit distribution coincides with the Brown measure of the operator quq.

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Authors and Affiliations

  1. Department for Mathematical Analysis, Budapest University of Technology and Economics, 1521, Budapest XI., Hungary

    Dénes Petz & Júlia Réffy

Authors
  1. Dénes Petz
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  2. Júlia Réffy
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Correspondence to Dénes Petz.

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Petz, D., Réffy, J. Large deviation for the empirical eigenvalue density of truncated Haar unitary matrices. Probab. Theory Relat. Fields 133, 175–189 (2005). https://doi.org/10.1007/s00440-004-0420-5

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  • Received: 29 October 2002

  • Revised: 30 November 2004

  • Published: 06 June 2005

  • Issue Date: October 2005

  • DOI: https://doi.org/10.1007/s00440-004-0420-5

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Keywords

  • Random matrices
  • Joint eigenvalue distribution
  • Haar unitary
  • Truncated Haar unitary
  • Large deviation
  • Rate function
  • Free probability
  • Random matrix model

Mathematics Subject Classification (2000)

  • 60F10
  • (15A52
  • 46L53
  • 60F05)
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