Approximation of Haar Distributed Matrices and Limiting Distributions of Eigenvalues of Jacobi Ensembles

@inproceedings{Jiang2007ApproximationOH,
  title={Approximation of Haar Distributed Matrices and Limiting Distributions of Eigenvalues of Jacobi Ensembles},
  author={Tiefeng Jiang},
  year={2007}
}
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. 
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