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Maxima of entries of Haar distributed matrices
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  • Published: 20 August 2004

Maxima of entries of Haar distributed matrices

  • Tiefeng Jiang1 

Probability Theory and Related Fields volume 131, pages 121–144 (2005)Cite this article

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Abstract.

Let Γ n =(γ ij ) be an n×n random matrix such that its distribution is the normalized Haar measure on the orthogonal group O(n). Let also W n :=max1≤ i , j ≤ n |γ ij |. We obtain the limiting distribution and a strong limit theorem on W n . A tool has been developed to prove these results. It says that up to n/( log n)2 columns of Γ n can be approximated simultaneously by those of some Y n =(y ij ) in which y ij are independent standard normals. Similar results are derived also for the unitary group U(n), the special orthogonal group SO(n), and the special unitary group SU(n).

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Authors and Affiliations

  1. School of Statistics, University of Minnesota, 313 Ford Hall, 224 Church Street S.E., Minneapolis, MN, 55455, USA

    Tiefeng Jiang

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  1. Tiefeng Jiang
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Correspondence to Tiefeng Jiang.

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Mathematics Subject Classification (2000):15A52, 60B10, 60B15, 60F10

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Jiang, T. Maxima of entries of Haar distributed matrices. Probab. Theory Relat. Fields 131, 121–144 (2005). https://doi.org/10.1007/s00440-004-0376-5

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  • Received: 01 May 2002

  • Revised: 17 March 2003

  • Published: 20 August 2004

  • Issue Date: January 2005

  • DOI: https://doi.org/10.1007/s00440-004-0376-5

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Keywords or phrases:

  • Haar measure
  • Maxima
  • Gram-Schmidt procedure
  • Large deviations
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