Operator Norm Upper Bound for Sub-Gaussian Tailed Random Matrices

Upper Bound for Intermediate Singular Values of Random Sub-Gaussian Matrices

Matrix Decompositions Using sub-Gaussian Random Matrices

In recent years, several algorithms which approximate matrix decomposition have been developed. These algorithms are based on metric conservation features for linear spaces of random projection types. We present a new algorithm, which achieves with high probability a rank-r SVD approximation of an n × n matrix and derive an error bound that does not depend on the first r singular values. Althou...

On the Spectral Norm of Gaussian Random Matrices

Let X be a d×d symmetric random matrix with independent but non-identically distributed Gaussian entries. It has been conjectured by Lata la that the spectral norm of X is always of the same order as the largest Euclidean norm of its rows. A positive resolution of this conjecture would provide a sharp understanding of the probabilistic mechanisms that control the spectral norm of inhomogeneous ...

Heavy-tailed random matrices

We discuss non-Gaussian random matrices whose elements are random variables with heavy-tailed probability distributions. In probability theory heavy tails of the distributions describe rare but violent events which usually have dominant influence on the statistics. They also completely change universal properties of eigenvalues and eigenvectors of random matrices. We concentrate here on the uni...

The Spectrum of Heavy Tailed Random Matrices

Take XN to be a symmetric matrix with real independent (modulo the symmetry constraint) equidistributed entries with law P and denote (λ1, · · · , λN) its eigenvalues. Then, Wigner [14] has shown that, if ∫ xdP (x) is finite, N−1 ∑N i=1 δλi/ √ N converges in expectation towards the semi-circle distribution. In this paper, we consider the case where P has a heavy tail and belong to the domain of...