相关论文: Application of Random Matrix Theory to Multivariat…

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 analyze complete spectra of the lattice Dirac operator in SU(2) gauge theory and demonstrate that the distribution of low-lying eigenvalues is described by random matrix theory. We present possible practical applications of this…

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 study a well-known problem concerning a random variable $Z$ uniformly distributed between two independent random variables. A new extension has been introduced for this problem and fairly large classes of randomly weighted average…

This work is concerned with finite range bounds on the variance of individual eigenvalues of random covariance matrices, both in the bulk and at the edge of the spectrum. In a preceding paper, the author established analogous results for…

We consider an inference on the eigenvalues of the covariance matrix of a multivariate normal distribution. The family of multivariate normal distributions with a fixed mean is seen as a Riemannian manifold with Fisher information metric.…

We investigate the spectral distribution of random matrix ensembles with correlated entries. We consider symmetric matrices with real valued entries and stochastically independent diagonals. Along the diagonals the entries may be…

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…

What is the connection of random matrices with integrable systems? Is this connection really useful? Introducing apprpriate times in the distribution of the ensemble of matrices, one shows that the corresponding distribution of the…

The focus of this survey paper is on the distribution function for the largest eigenvalue in the finite N Gaussian ensembles (GOE,GUE,GSE) in the edge scaling limit of N->infinity. These limiting distribution functions are expressible in…

This article is an introductory review of random matrix theory (RMT) and its applications, with special focus on quantum chaos. Random matrices were first used by Wigner to understand the spectra of complex nuclei from a statistical…

Using the superstatistics method, we propose an extension of the random matrix theory to cover systems with mixed regular-chaotic dynamics. Unlike most of the other works in this direction, the ensembles of the proposed approach are basis…

Random matrix theory is finding an increasing number of applications in the context of information theory and communication systems, especially in studying the properties of complex networks. Such properties include short-term and long-term…

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…

Relying on recent advances in statistical estimation of covariance distances based on random matrix theory, this article proposes an improved covariance and precision matrix estimation for a wide family of metrics. The method is shown to…

We extend classical time-frequency limiting analysis, historically applied to one-dimensional finite signals, to the multidimensional discrete setting. This extension is relevant for images, videos, and other multidimensional signals, as it…

We propose a novel method for analysis of experimental data obtained at relativistic nucleus-nucleus collisions. The method, based on the ideas of Random Matrix Theory, is applied to detect systematic errors that occur at measurements of…

We study the asymptotic distribution of the eigenvalues of random Hermitian periodic band matrices, focusing on the spectral edges. The eigenvalues close to the edges converge in distribution to the Airy point process if (and only if) the…

In this paper we develop a complete analytical framework based on Random Matrix Theory for the performance evaluation of Eigenvalue-based Detection. While, up to now, analysis was limited to false-alarm probability, we have obtained an…