Approximation of Haar distributed matrices and limiting distributions of eigenvalues of Jacobi ensembles

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Abstract

We develop a tool to approximate the entries of a large dimensional complex Jacobi ensemble with independent complex Gaussian random variables. Based on this and the author's earlier work in this direction, we obtain the Tracy-Widom law of the largest singular values of the Jacobi emsemble. Moreover, the circular law, the Marchenko-Pastur law, the central limit theorem, and the laws of large numbers for the spectral norms are also obtained.

Original languageEnglish (US)
Pages (from-to)221-246
Number of pages26
JournalProbability Theory and Related Fields
Volume144
Issue number1-2
DOIs
StatePublished - May 2009

Keywords

  • Eigenvalue
  • Empirical distribution
  • Haar measure
  • Largest eigenvalue
  • Limiting distribution
  • Random matrix

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