Bernoulli

  • Bernoulli
  • Volume 19, Number 3 (2013), 1028-1046.

Limit theorems for beta-Jacobi ensembles

Tiefeng Jiang

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Abstract

For a $\beta$-Jacobi ensemble determined by parameters $a_{1}$, $a_{2}$ and $n$, under the restriction that the three parameters go to infinity with $n$ and $a_{1}$ being of small orders of $a_{2}$, we obtain some limit theorems about the eigenvalues. In particular, we derive the asymptotic distributions for the largest and the smallest eigenvalues, the central limit theorems of the eigenvalues, and the limiting distributions of the empirical distributions of the eigenvalues.

Article information

Source
Bernoulli Volume 19, Number 3 (2013), 1028-1046.

Dates
First available in Project Euclid: 26 June 2013

Permanent link to this document
https://projecteuclid.org/euclid.bj/1372251152

Digital Object Identifier
doi:10.3150/12-BEJ495

Mathematical Reviews number (MathSciNet)
MR3079305

Zentralblatt MATH identifier
1278.60013

Keywords
beta-ensemble empirical distribution Jacobi ensemble Laguerre ensemble largest eigenvalue limiting distribution random matrix random operator smallest eigenvalue

Citation

Jiang, Tiefeng. Limit theorems for beta-Jacobi ensembles. Bernoulli 19 (2013), no. 3, 1028--1046. doi:10.3150/12-BEJ495. https://projecteuclid.org/euclid.bj/1372251152


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