Related papers: Eigenvector Delocalization for Non-Hermitian Rando…

We establish bounds on the spectral radii for a large class of sparse random matrices, which includes the adjacency matrices of inhomogeneous Erd\H{o}s-R\'enyi graphs. Our error bounds are sharp for a large class of sparse random matrices.…

We consider products of independent square non-Hermitian random matrices. More precisely, let X(1),...,X(n) be random matrices with independent entries (real or complex with independent real and imaginary parts) with zero mean and variance…

We establish strong dynamical localization for a class of multi-particle Anderson models in a Euclidean space with an alloy-type random potential and a sub-exponentially decaying interaction of infinite range. For the first time in the…

We examine the empirical distribution of the eigenvalues and the eigenvectors of adjacency matrices of sparse regular random graphs. We find that when the degree sequence of the graph slowly increases to infinity with the number of…

In this paper, we investigate the eigenvalue problem for a non-local dispersal operator defined on a bounded spatial domain with Neumann-type boundary conditions. Unlike the classical Laplacian, the non-local operator lacks compactness,…

We prove localization and probabilistic bounds on the minimum level spacing for the Anderson tight-binding model on the lattice in any dimension, with single-site potential having a discrete distribution taking N values, with N large.

Many classical Computer Vision problems, such as essential matrix computation and pose estimation from 3D to 2D correspondences, can be solved by finding the eigenvector corresponding to the smallest, or zero, eigenvalue of a matrix…

The diagonalization of matrices may be the top priority in the application of modern physics. In this paper, we numerically demonstrate that, for real symmetric random matrices with non-positive off-diagonal elements, a universal scaling…

We propose a new method for computing the eigenvalue decomposition of a dense real normal matrix $A$ through the decomposition of its skew-symmetric part. The method relies on algorithms that are known to be efficiently implemented, such as…

A recent development in studies of random non-Hermitian quantum systems is reviewed. Delocalization was found to occur under a sufficiently large constant imaginary vector potential even in one and two dimensions. The phenomenon has a…

We consider the limiting location and limiting distribution of the largest eigenvalue in real symmetric ($\beta$ = 1), Hermitian ($\beta$ = 2), and Hermitian self-dual ($\beta$ = 4) random matrix models with rank 1 external source. They are…

Eigenvalue estimates that are optimal in some sense have self-evident appeal and leave estimators with a sense of virtue and economy. So, it is natural that ongoing searches for effective strategies for difficult tasks such as estimating…

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…

The purpose of the present work is to establish decorrelation estimates for the locally renormalized eigenvalues of the discrete Anderson model near two distinct energies inside the localization region. In dimension one, we prove these…

Rank-constrained matrix problems appear frequently across science and engineering. The convergence analysis of iterative algorithms developed for these problems often hinges on local error bounds, which correlate the distance to the…

In an instance of the minimum eigenvalue problem, we are given a collection of $n$ vectors $v_1,\ldots, v_n \subset {\mathbb{R}^d}$, and the goal is to pick a subset $B\subseteq [n]$ of given vectors to maximize the minimum eigenvalue of…

We consider $N\times N$ symmetric random matrices where the probability distribution for each matrix element is given by a measure $\nu$ with a subexponential decay. We prove that the eigenvalue spacing statistics in the bulk of the…

We study the problem of approximating the eigenspectrum of a symmetric matrix $\mathbf A \in \mathbb{R}^{n \times n}$ with bounded entries (i.e., $\|\mathbf A\|_{\infty} \leq 1$). We present a simple sublinear time algorithm that…

We calculate analytically the probability of large deviations from its mean of the largest (smallest) eigenvalue of random matrices belonging to the Gaussian orthogonal, unitary and symplectic ensembles. In particular, we show that the…

In this paper, we study the eigenvalues and eigenvectors of the spiked invariant multiplicative models when the randomness is from Haar matrices. We establish the limits of the outlier eigenvalues $\widehat{\lambda}_i$ and the generalized…