Related papers: Random Subsets of Structured Deterministic Frames …

In random matrix theory, Marchenko-Pastur law states that random matrices with independent and identically distributed entries have a universal asymptotic eigenvalue distribution under large dimension limit, regardless of the choice of…

We consider the singular values of certain Young diagram shaped random matrices. For block-shaped random matrices, the empirical distribution of the squares of the singular eigenvalues converges almost surely to a distribution whose moments…

We equip the polytope of $n\times n$ Markov matrices with the normalized trace of the Lebesgue measure of $\mathbb{R}^{n^2}$. This probability space provides random Markov matrices, with i.i.d. rows following the Dirichlet distribution of…

We consider the singular vectors of any $m \times n$ submatrix of a rectangular $M \times N$ Gaussian matrix and study their asymptotic overlaps with those of the full matrix, in the macroscopic regime where $N \,/\, M\,$, $m \,/\, M$ as…

We propose to study unitary matrix ensembles defined in terms of unitary stochastic transition matrices associated with Markov processes on graphs. We argue that the spectral statistics of such an ensemble (after ensemble averaging) depends…

The celebrated Mar\v{c}enko-Pastur law, that considers the asymptotic spectral density of random covariance matrices, has found a great number of applications in physics, biology, economics, engineering, among others. Here, using techniques…

In this paper, we investigate the limiting spectral distribution of the sample correlation matrix, whose sample vectors are $k$-fold tensor products of $n$-dimensional vectors with i.i.d. entries. We focus on the limiting regime $n,k \to…

The traditional class of elliptical distributions is extended to allow for asymmetries. A completely robust dispersion matrix estimator (the `spectral estimator') for the new class of `generalized elliptical distributions' is presented. It…

We consider random matrices whose entries are f(<Xi,Xj>) or f(||Xi-Xj||^2) for iid vectors Xi in R^p with normalized distribution. Assuming that f is sufficiently smooth and the distribution of Xi's is sufficiently nice, El Karoui [17]…

In statistics, assuming samples are independent is reasonable. However, this property can fail to hold for the features, a distinction that has led to several lines of work aiming to remove the latter assumption of independence present in…

We consider a problem in random matrix theory that is inspired by quantum information theory: determining the largest eigenvalue of a sum of p random product states in (C^d)^{otimes k}, where k and p/d^k are fixed while d grows. When k=1,…

Using the Coulomb gas method and standard methods of statistical physics, we compute analytically the joint cumulative probability distribution of the extreme eigenvalues of the Jacobi-MANOVA ensemble of random matrices, in the limit of…

We take on a Random Matrix theory viewpoint to study the spectrum of certain reversible Markov chains in random environment. As the number of states tends to infinity, we consider the global behavior of the spectrum, and the local behavior…

Estimating the eigenvalues of a population covariance matrix from a sample covariance matrix is a problem of fundamental importance in multivariate statistics; the eigenvalues of covariance matrices play a key role in many widely…

This paper is a variation on the uniform spanning tree theme. We use random spanning forests to solve the following problem: for a Markov process on a finite set of size $n$, find a probability law on the subsets of any given size $m \leq…

We consider classical shadows of fermion wavefunctions with $\eta$ particles occupying $n$ modes. We prove that all $k$-Reduced Density Matrices (RDMs) may be simultaneously estimated to an average variance of $\epsilon^{2}$ using at most…

We study the eigenvalue distributions for sums of independent rank-one $k$-fold tensor products of large $n$-dimensional vectors. Previous results in the literature assume that $k=o(n)$ and show that the eigenvalue distributions converge to…

We compute the full probability distribution of the spectral form factor in the self-dual kicked Ising model by providing an exact lower bound for each moment and verifying numerically that the latter is saturated. We show that at large…

In this paper, we investigate the limiting empirical spectral distribution (LSD) of sums of independent rank-one $k$-fold tensor products of $n$-dimensional vectors as $k,n \to \infty$. Assuming that the base vectors are complex random…

We consider $m$ spinless Bosons distributed over $l$ degenerate single-particle states and interacting through a $k$-body random interaction with Gaussian probability distribution (the Bosonic embedded $k$-body ensembles). We address the…