Related papers: On eigenvector statistics in the spherical and tru…
The perturbed GUE corners ensemble is the joint distribution of eigenvalues of all principal submatrices of a matrix $G+\mathrm{diag}(\mathbf{a})$, where $G$ is the random matrix from the Gaussian Unitary Ensemble (GUE), and…
We analytically compute the large-deviation probability of a diagonal matrix element of two cases of random matrices, namely $\beta=[\vec H^\dagger\vec H]^{-1}_{11}$ and $\gamma=[\vec I_N+\rho\vec H^\dagger\vec H]^{-1}_{11}$, where $\vec H$…
In the present work we show that the joint probability distribution of the eigenvalues can be expressed in terms of a differential operator acting on the distribution of some other matrix quantities. Those quantities might be the diagonal…
We compute asymptotic non-linear shrinkage formulas for covariance and precision matrix estimators for weighted sample covariances, and the joint sample-population eigenvector overlap distribution, in the spirit of Ledoit and P\'ech\'e. We…
This paper investigates limiting properties of eigenvalues of multivariate sample spatial-sign covariance matrices when both the number of variables and the sample size grow to infinity. The underlying p-variate populations are general…
The empirical eigenvalue distribution of the elliptic random matrix ensemble tends to the uniform measure on an ellipse in the complex plane as its dimension tends to infinity. We show this convergence on all mesoscopic scales slightly…
We study eigenvalue distribution of the adjacency matrix $A^{(N,p, \alpha)}$ of weighted random bipartite graphs $\Gamma= \Gamma_{N,p}$. We assume that the graphs have $N$ vertices, the ratio of parts is $\frac{\alpha}{1-\alpha}$ and the…
We develop an algorithm for sampling from the unitary invariant random matrix ensembles. The algorithm is based on the representation of their eigenvalues as a determinantal point process whose kernel is given in terms of orthogonal…
We study random points on the real line generated by the eigenvalues in unitary invariant random matrix ensembles or by more general repulsive particle systems. As the number of points tends to infinity, we prove convergence of the…
We study the eigenvector mass distribution of an $N\times N$ Wigner matrix on a set of coordinates $I$ satisfying $| I | \ge c N$ for some constant $c >0$. For eigenvectors corresponding to eigenvalues at the spectral edge, we show that the…
Using numerical exact diagonalization, we study matrix elements of a local spin operator in the eigenbasis of two different nonintegrable quantum spin chains. Our emphasis is on the question to what extent local operators can be represented…
We study the eigenvalue distribution of a random matrix, at a transition where a new connected component of the eigenvalue density support appears away from other connected components. Unlike previously studied critical points, which…
We consider $N\times N$ symmetric or hermitian random matrices with independent, identically distributed entries where the probability distribution for each matrix element is given by a measure $\nu$ with a subexponential decay. We prove…
The focus of this paper is on the distribution function of the rightmost eigenvalue for the complex elliptic Ginibre ensemble in the limit of weak non-Hermiticity. We show how the limiting distribution function can be expressed in terms of…
Complex eigenvalues of random matrices $J=\text{GUE }+ i\gamma \diag (1, 0, \ldots, 0)$ provide the simplest model for studying resonances in wave scattering from a quantum chaotic system via a single open channel. It is known that in the…
We show that the empirical eigenvalue measure for sum of $d$ independent Haar distributed $n$-dimensional unitary matrices, converge for $n \to \infty$ to the Brown measure of the free sum of $d$ Haar unitary operators. The same applies for…
Kolo\u{g}lu, Kopp and Miller compute the limiting spectral distribution of a certain class of real random matrix ensembles, known as $k$-block circulant ensembles, and discover that it is exactly equal to the eigenvalue distribution of an…
The eigenvalue density for members of the Gaussian orthogonal and unitary ensembles follows the Wigner semi-circle law. If the Gaussian entries are all shifted by a constant amount c/Sqrt(2N), where N is the size of the matrix, in the large…
In an attempt to characterize the structure of eigenvectors of random regular graphs, we investigate the correlations between the components of the eigenvectors associated to different vertices. In addition, we provide numerical…
A multifractal analysis is performed on the universality classes of random matrices and the transition ones.Our results indicate that the eigenvector probability distribution is a linear sum of two chi-squared distribution throughout the…