相关论文: Asymptotics of random density matrices
A density matrix describes the statistical state of a quantum system. It is a powerful formalism to represent both the quantum and classical uncertainty of quantum systems and to express different statistical operations such as measurement,…
This paper discusses the approximate distributions of eigenvalues of a singular Wishart matrix. We give the approximate joint density of eigenvalues by Laplace approximation for the hyper-geometric functions of matrix arguments.…
The spectral densities of ensembles of non-Hermitian sparse random matrices are analysed using the cavity method. We present a set of equations from which the spectral density of a given ensemble can be efficiently and exactly calculated.…
We describe Generalized Hermitian matrices ensemble sometimes called Chiral ensemble. We give global asymptotic of the density of eigenvalues or the statistical density. We will calculate a Laplace transform of such a density for finite…
Results on the spectral behavior of random matrices as the dimension increases are applied to the problem of detecting the number of sources impinging on an array of sensors. A common strategy to solve this problem is to estimate the…
In this monograph, we prove an asymptotic approximation for integrals of probability densities over sets in finite dimensional euclidean space, which are far away from the origin (asymptotic sets). We use this approximation to investigate…
The asymptotic normality for a large family of eigenvalue statistics of a general sample covariance matrix is derived under the ultra-high dimensional setting, that is, when the dimension to sample size ratio $p/n \to \infty$. Based on this…
The purpose of this article is to present a general method to find limiting laws for some renormalized statistics on random permutations. The model considered here is Ewens sampling model, which generalizes uniform random permutations. We…
The spectra of empirical correlation matrices, constructed from multivariate data, are widely used in many areas of sciences, engineering and social sciences as a tool to understand the information contained in typically large datasets. In…
This paper concentrates on asymptotic properties of determinants of some random symmetric matrices. If B_{n,r} is a n x r rectangular matrix and B_{n,r}' its transpose, we study det (B_{n,r}'B_{n,r}) when n,r tends to infinity with r/n \to…
We analyze statistical properties of complex eigenvalues of random matrices $\hat{A}$ close to unitary. Such matrices appear naturally when considering quantized chaotic maps within a general theory of open linear stationary systems with…
For a broad class of unitary ensembles of random matrices we demonstrate the universal nature of the Janossy densities of eigenvalues near the spectral edge, providing a different formulation of the probability distributions of the limiting…
We investigate the level density for several ensembles of positive random matrices of a Wishart--like structure, $W=XX^{\dagger}$, where $X$ stands for a nonhermitian random matrix. In particular, making use of the Cauchy transform, we…
Modularity is a popular metric for quantifying the degree of community structure within a network. The distribution of the largest eigenvalue of a network's edge weight or adjacency matrix is well studied and is frequently used as a…
The eigenvalues and eigenvectors of the connectivity matrix of complex networks contain information about its topology and its collective behavior. In particular, the spectral density $\rho(\lambda)$ of this matrix reveals important network…
In this paper, we investigate the spectral properties of the adjacency and the Laplacian matrices of random graphs. We prove that: (i) the law of large numbers for the spectral norms and the largest eigenvalues of the adjacency and the…
In this paper we consider random block matrices, which generalize the general beta ensembles, which were recently investigated by Dumitriu and Edelmann (2002, 2005). We demonstrate that the eigenvalues of these random matrices can be…
We use the well-known isomorphism between operator algebras and function spaces equipped with a star product to study the asymptotic properties of certain matrix sequences in which the matrix dimension $D$ tends to infinity. Our approach is…
Random matrix theory allows one to deduce the eigenvalue spectrum of a large matrix given only statistical information about its elements. Such results provide insight into what factors contribute to the stability of complex dynamical…
The universal connected correlations proposed recently between eigenvalues of unitary random matrices is examined numerically. We perform an ensemble average by the Monte Carlo sampling. Although density of eigenvalues and a bare…