Related papers: First colonization of a hard-edge in random matrix…
We use an extension of the diagrammatic rules in random matrix theory to evaluate spectral properties of finite and infinite products of large complex matrices and large hermitian matrices. The infinite product case allows us to define a…
The open problem of calculating the limiting spectrum (or its Shannon transform) of increasingly large random Hermitian finite-band matrices is described. In general, these matrices include a finite number of non-zero diagonals around their…
We apply concepts of random differential geometry connected to the random matrix ensembles of the random linear operators acting on finite dimensional Hilbert spaces. The values taken by random linear operators belong to the Liouville…
A class of robust estimators of scatter applied to information-plus-impulsive noise samples is studied, where the sample information matrix is assumed of low rank; this generalizes the study of (Couillet et al., 2013b) to spiked random…
Let $A$ be a $n\times n$ complex Hermitian matrix and let $\lambda(A)=(\lambda_1,\ldots,\lambda_n)\in \mathbb{R}^n$ denote the eigenvalues of $A$, counting multiplicities and arranged in non-increasing order. Motivated by problems arising…
Given a length function on the edge set of a finite graph, we define a vertex-weight and an edge-weight in terms of it and consider the corresponding graph Laplacian. In this paper, we consider the problem of maximizing the first nonzero…
The first paper in this series introduced a new family of nonasymptotic matrix concentration inequalities that sharply capture the spectral properties of very general random matrices in terms of an associated noncommutative model. These…
In this paper the question about statistical properties of block--hierarchical random matrices is raised for the first time in connection with structural characteristics of random hierarchical networks obtained by mipmapping procedure. In…
Let $A$ be an $n\times n$ matrix with iid entries where $A_{ij} \sim \mathrm{Ber}(p)$ is a Bernoulli random variable with parameter $p = d/n$. We show that the empirical measure of the eigenvalues converges, in probability, to a…
In this article, we study high-dimensional behavior of empirical spectral distributions $\{L_N(t), t\in[0,T]\}$ for a class of $N\times N$ symmetric/Hermitian random matrices, whose entries are generated from the solution of stochastic…
Statistical properties of ensembles of random density matrices are investigated. We compute traces and von Neumann entropies averaged over ensembles of random density matrices distributed according to the Bures measure. The eigenvalues of…
The eigenvalue distribution of the sum of two large Hermitian matrices, when one of them is conjugated by a Haar distributed unitary matrix, is asymptotically given by the free convolution of their spectral distributions. We prove that this…
Complex extension of quantum mechanics and the discovery of pseudo-unitarily invariant random matrix theory has set the stage for a number of applications of these concepts in physics. We briefly review the basic ideas and present…
We consider highly heterogeneous random networks with symmetric interactions in the limit of high connectivity. A key feature of this system is that the spectral density of the corresponding ensemble exhibits a divergence within the bulk.…
This paper deals with symmetric random matrices whose upper diagonal entries are obtained from a linear random field with heavy tailed noise. It is shown that the maximum eigenvalue and the spectral radius of such a random matrix with…
We study a new random matrix ensemble $X$ which is constructed by an application of a two dimensional linear filter to a matrix of iid random variables with infinite fourth moments. Our result gives asymptotic lower and upper bounds for the…
The spectra of random feature matrices provide essential information on the conditioning of the linear system used in random feature regression problems and are thus connected to the consistency and generalization of random feature models.…
We consider a discrete, non-Hermitian random matrix model, which can be expressed as a shift of a rank-one perturbation of an anti-symmetric matrix. We show that, asymptotically almost surely, the real parts of the eigenvalues of the…
We consider the eigenvalue problem for the case where the input matrix is symmetric and its entries perturb in some given intervals. We present a characterization of some of the exact boundary points, which allows us to introduce an inner…
Eigenvalues statistics of various many-body systems have been widely studied using the nearest neighbor spacing distribution under the random matrix theory framework. Here, we numerically analyze eigenvalue ratio statistics of multiplex…