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

Abstract: I will first present tools to approximate the entries of a large dimensional real and complex Jacobi ensembles with independent complex Gaussian random variables. Based on this, 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.

Hosted by: Xiaoming Huo