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On spectral measures of random Jacobi matrices

Research paper by Trinh Khanh Duy

Indexed on: 22 Jun '16Published on: 22 Jun '16Published in: Mathematics - Probability



Abstract

The paper studies the limiting behaviour of spectral measures of random Jacobi matrices of Gaussian, Wishart and MANOVA beta ensembles. We show that the spectral measures converge weakly to a limit distribution which is the semicircle distribution, Marchenko-Pastur distributions or Kesten-Mckey distributions, respectively. The Gaussian fluctuation around the limit is then investigated.