This thesis focuses on several fundamental classes of random matrices with independent entries - Wigner matrices, random band matrices, and adjacency matrices of sparse random graphs. The results fall roughly into two two classes: local laws, which provide strong control of the eigenvalue density down to small spectral scales, and the study of mesoscopic linear eigenvalue statistics
This is a continuation of our earlier paper (Tao and Vu, http://arxiv.org/abs/090...
Spectra of sparse non-Hermitian random matrices determine the dynamics of complex processes on graph...
We consider general self-adjoint polynomials in several independent random matrices whose entries ar...
We consider spectral properties and the edge universality of sparse random matrices, the class of ra...
These notes provide an introduction to the local semicircle law from random matrix theory, as well a...
We develop a new method for deriving local laws for a large class of random matrices. It is applicab...
We prove a local law in the bulk of the spectrum for random Gram matrices XX∗, a generalization of s...
We consider the spectral statistics of large random band matrices on mesoscopic energy scales. We sh...
We consider the spectral statistics of large random band matrices on mesoscopic energy scales. We sh...
We consider the spectral statistics of large random band matrices on mesoscopic energy scales. We sh...
Abstract. We study the universality of the eigenvalue statistics of the covariance matrices
We consider the spectral statistics of large random band matrices on mesoscopic energy scales. We sh...
We consider large random matrices with a general slowly decaying correlation among its entries. We p...
In order to have a better understanding of finite random matrices with non-Gaussian entries, we stud...
We present a generalization of the method of the local relaxation flow to establish the universality...
This is a continuation of our earlier paper (Tao and Vu, http://arxiv.org/abs/090...
Spectra of sparse non-Hermitian random matrices determine the dynamics of complex processes on graph...
We consider general self-adjoint polynomials in several independent random matrices whose entries ar...
We consider spectral properties and the edge universality of sparse random matrices, the class of ra...
These notes provide an introduction to the local semicircle law from random matrix theory, as well a...
We develop a new method for deriving local laws for a large class of random matrices. It is applicab...
We prove a local law in the bulk of the spectrum for random Gram matrices XX∗, a generalization of s...
We consider the spectral statistics of large random band matrices on mesoscopic energy scales. We sh...
We consider the spectral statistics of large random band matrices on mesoscopic energy scales. We sh...
We consider the spectral statistics of large random band matrices on mesoscopic energy scales. We sh...
Abstract. We study the universality of the eigenvalue statistics of the covariance matrices
We consider the spectral statistics of large random band matrices on mesoscopic energy scales. We sh...
We consider large random matrices with a general slowly decaying correlation among its entries. We p...
In order to have a better understanding of finite random matrices with non-Gaussian entries, we stud...
We present a generalization of the method of the local relaxation flow to establish the universality...
This is a continuation of our earlier paper (Tao and Vu, http://arxiv.org/abs/090...
Spectra of sparse non-Hermitian random matrices determine the dynamics of complex processes on graph...
We consider general self-adjoint polynomials in several independent random matrices whose entries ar...
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