Maxima of entries of Haar distributed matrices

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Abstract

Let Γn = (γij) be an x n random matrix such that its distribution is the normalized Haar measure on the orthogonal group O(n). Let also Wn := max1≤i, j≤nij|. We obtain the limiting distribution and a strong limit theorem on Wn. A tool has been developed to prove these results. It says that up to n/(log n)2 columns of Γn can be approximated simultaneously by those of some Yn = (yij) in which yij 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). -

Original languageEnglish (US)
Pages (from-to)121-144
Number of pages24
JournalProbability Theory and Related Fields
Volume131
Issue number1
DOIs
StatePublished - Jan 2005

Keywords

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

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