Related papers: Eigenvalue Distributions in Matrix Models for Cher…

The problem of iterated partial summations is solved for some discrete distributions defined on discrete supports. The power method, usually used as a computational approach to finding matrix eigenvalues and eigenvectors, is in some cases…

We study the central limit theorem (CLT) for linear eigenvalue statistics of several types of matrix models, whose entries are having exploding moments, i.e., moments of the entries are increasing with the size of the matrix. In particular,…

Let A be a p-variate real Wishart matrix on n degrees of freedom with identity covariance. The distribution of the largest eigenvalue in A has important applications in multivariate statistics. Consider the asymptotics when p grows in…

We studied numerically the distribution of the entanglement Hamiltonian eigenvalues in two one-dimensional free fermion models and the typical three-dimensional Anderson model. We showed numerically that this distribution depends on the…

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…

We study ensembles of random symmetric matrices whose entries exhibit certain correlations. Examples are distributions of Curie-Weiss-type. We provide a criterion on the correlations ensuring the validity of Wigner's semicircle law for the…

Finding eigenvalue distributions for a number of sparse random matrix ensembles can be reduced to solving nonlinear integral equations of the Hammerstein type. While a systematic mathematical theory of such equations exists, it has not been…

We study the universal properties of distributions of eigenvalues of random matrices in the large $N$ limit. The distributions fall in universality classes characterized entirely by the support of the spectral density.

This paper aims to derive asymptotical distributions of the spiked eigenvalues of the large-dimensional spiked Fisher matrices without Gaussian assumption and the restrictive assumptions on covariance matrices. We first establish invariance…

This article provides a central limit theorem for a consistent estimator of population eigenvalues with large multiplicities based on sample covariance matrices. The focus is on limited sample size situations, whereby the number of…

In \cite{Diaz} beta type I and II doubly singular distributions were introduced and their densities and the joint densities of nonzero eigenvalues were derived. In such matrix variate distributions $p$, the dimension of two singular Wishart…

We study a class of random matrices that appear in several communication and signal processing applications, and whose asymptotic eigenvalue distribution is closely related to the reconstruction error of an irregularly sampled bandlimited…

We study ${\cal N}=3$ linear Chern-Simons-matter theories in the planar limit. The matter content of the theory is depicted by a linear-shape diagram with $n$ nodes and $n-1$ links for any $n$. The free energy and the vevs of BPS Wilson…

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…

The eigenvalue spacing of a uniformly chosen random finite unipotent matrix in its permutation action on lines is studied. We obtain bounds for the mean number of eigenvalues lying in a fixed arc of the unit circle and offer an approach…

Probabilistic estimates on linear combinations of eigenvalues of the one dimensional Anderson model are derived. So far only estimates on the density of eigenvalues and of pairs were found by Wegner and by Minami. Our work was motivated by…

We study a mathematical model of a hinged flexible beam with piezoelectric actuators and electromagnetic shaker in this paper. The shaker is modelled as a mass and spring system attached to the beam. To analyze free vibrations of this…

This paper summarizes some work I've been doing on eigenvalue correlators of Random Matrix Models which show some interesting behaviour. First we consider matrix models with gaps in there spectrum or density of eigenvalues. The…

This paper focuses on investigating Stein's invariant shrinkage estimators for large sample covariance matrices and precision matrices in high-dimensional settings. We consider models that have nearly arbitrary population covariance…

Assume a finite set of complex random variables form a determinantal point process, we obtain a theorem on the limit of the empirical distribution of these random variables. The result is applied to %We study the limits of the empirical…