Related papers: Random matrices acting on sets: Independent column…

Diagrammatic techniques to compute perturbatively the spectral properties of Euclidean Random Matrices in the high-density regime are introduced and discussed in detail. Such techniques are developed in two alternative and very different…

We study block-diagonal random matrices with i.i.d. subexponential entries and show that, despite their highly structured form, they already guarantee exact sparse recovery from a nearly optimal number of measurements. When the matrix…

We consider Markov chains with random transition probabilities which, moreover, fluctuate randomly with time. We describe such a system by a product of stochastic matrices, $U(t)=M_t\cdots M_1$, with the factors $M_i$ drawn independently…

Products of random $2\times 2$ matrices exhibit Gaussian fluctuations around almost surely convergent Lyapunov exponents. In this paper, the distribution of the random matrices is supported by a small neighborhood of order $\lambda>0$ of…

We show that the operatorial framework developed by Voiculescu for free random variables can be extended to arrays of random variables whose multiplication imitates matricial multiplication. The associated notion of independence, called…

Motivated by problems in controlled experiments, we study the discrepancy of random matrices with continuous entries where the number of columns $n$ is much larger than the number of rows $m$. Our first result shows that if $\omega(1) = m =…

We apply random matrix theory to complex networks. We show that nearest neighbor spacing distribution of the eigenvalues of the adjacency matrices of various model networks, namely scale-free, small-world and random networks follow…

We study the asymptotic distribution of level crossings for random matrix pencils A_n+\lambda B_n in several ensembles, including complex and real i.i.d. matrices and Gaussian/Hermitian settings. We derive a representation of the normalized…

It has been observed that the performances of many high-dimensional estimation problems are universal with respect to underlying sensing (or design) matrices. Specifically, matrices with markedly different constructions seem to achieve…

A central question in random matrix theory is universality. When an emergent phenomena is observed from a large collection of chosen random variables it is natural to ask if this behavior is specific to the chosen random variable or if the…

In order to have a better understanding of finite random matrices with non-Gaussian entries, we study the $1/N$ expansion of local eigenvalue statistics in both the bulk and at the hard edge of the spectrum of random matrices. This gives…

We propose a randomized method for solving linear programs with a large number of columns but a relatively small number of constraints. Since enumerating all the columns is usually unrealistic, such linear programs are commonly solved by…

Continuing with the authors concept (and results) of defining independence for columns of a boolean and superboolean matrix, we apply this theory to finite lattices and finite posets, introducing boolean and superboolean matrix…

In this note, we define a Gaussian probability distribution over matrices. We prove some useful properties of this distribution, namely, the fact that marginalization, conditioning, and affine transformations preserve the matrix Gaussian…

We investigate the sub-Gaussian property for almost surely bounded random variables. If sub-Gaussianity per se is de facto ensured by the bounded support of said random variables, then exciting research avenues remain open. Among these…

We consider the Gaussian ensembles of random matrices and describe the normal modes of the eigenvalue spectrum, i.e., the correlated fluctuations of eigenvalues about their most probable values. The associated normal mode spectrum is…

Let $X=C+\mathrm{E}$ with a deterministic matrix $C\in\R^{M\times M}$ and $\mathrm{E}$ some centered Gaussian $M\times M$-matrix whose entries are independent with variance $\sigma^2$. In the present work, the accuracy of reduced-rank…

This paper establishes a new comparison principle for the minimum eigenvalue of a sum of independent random positive-semidefinite matrices. The principle states that the minimum eigenvalue of the matrix sum is controlled by the minimum…

We address overcrowding estimates for the singular values of random iid matrices, as well as for the eigenvalues of random Wigner matrices. We show evidence of long range separation under arbitrary perturbation even in matrices of discrete…

We study subset selection for matrices defined as follows: given a matrix $\matX \in \R^{n \times m}$ ($m > n$) and an oversampling parameter $k$ ($n \le k \le m$), select a subset of $k$ columns from $\matX$ such that the pseudo-inverse of…