Spectral Analysis of Large Dimensional Random Matrices

  title={Spectral Analysis of Large Dimensional Random Matrices},
  author={Zhidong Bai and Jack W. Silverstein},
Wigner Matrices and Semicircular Law.- Sample Covariance Matrices and the Mar#x010D enko-Pastur Law.- Product of Two Random Matrices.- Limits of Extreme Eigenvalues.- Spectrum Separation.- Semicircular Law for Hadamard Products.- Convergence Rates of ESD.- CLT for Linear Spectral Statistics.- Eigenvectors of Sample Covariance Matrices.- Circular Law.- Some Applications of RMT. 
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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
CLT for spectra of submatrices of Wigner random matrices
We prove a CLT for spectra of submatrices of real symmetric and Hermitian Wigner matrices. We show that if in the standard normalization the fourth moment of the off-digonal entries is GOE/GUE-like
Asymptotic Freeness for Rectangular Random Matrices and Large Deviations for Sample Covariance Matrices With Sub-Gaussian Tails
We establish a large deviation principle for the empirical spectral measure of a sample covariance matrix with sub-Gaussian entries, which extends Bordenave and Caputo's result for Wigner matrices
The spectral norm of random inner-product kernel matrices
We study an “inner-product kernel” random matrix model, whose empirical spectral distribution was shown by Xiuyuan Cheng and Amit Singer to converge to a deterministic measure in the large n and p
Second-Order Moment Convergence Rates for Spectral Statistics of Random Matrices
The precise second-order moment convergence rates of a type of series constructed by the spectral statistics of Wigner matrices or sample covariance matrices are established.
Borders on the expected $2$-Wasserstein distance between the empirical spectral measure and the semicircle law are derived and results are available for random covariance matrices.
Eigenvalue variance bounds for Wigner random matrices
Borders on the expected $2$-Wasserstein distance between the empirical spectral measure and the semicircle law are derived and extended to families of Hermitian Wigner matrices by means of the Tao and Vu Four Moment Theorem and recent localization results.
Random matrices: Universality of local eigenvalue statistics
In this paper, we consider the universality of the local eigenvalue statistics of random matrices. Our main result shows that these statistics are determined by the first four moments of the