Related papers: Asymptotics of eigenstructure of sample correlatio…
We consider the asymptotic fluctuation behavior of the largest eigenvalue of certain sample covariance matrices in the asymptotic regime where both dimensions of the corresponding data matrix go to infinity. More precisely, let $X$ be an…
We study the asymptotic behavior of the spectra of matrices of the form $S_n = \frac{1}{n}XX^*$ where $X =\sum_{r=1}^K X_r$, where $X_r = A_r^\frac{1}{2}Z_rB_r^\frac{1}{2}$, $K \in \mathbb{N}$ and $A_r,B_r$ are sequences of positive…
We show that correlation matrices with particular average and variance of the correlation coefficients have a notably restricted spectral structure. Applying geometric methods, we derive lower bounds for the largest eigenvalue and the…
We consider the empirical eigenvalue distribution of random real symmetric matrices with stochastically independent skew-diagonals and study its limit if the matrix size tends to infinity. We allow correlations between entries on the same…
We consider two types of spiked multivariate F distributions: a scaled distribution with the scale matrix equal to a rank-one perturbation of the identity, and a distribution with trivial scale, but rank-one non-centrality. The norm of the…
We investigate the asymptotics of eigenvalues of sample covariance matrices associated with a class of non-independent Gaussian processes (separable and temporally stationary) under the Kolmogorov asymptotic regime. The limiting spectral…
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…
Correlation function of complex eigenvalues of N by N random matrices drawn from non-Hermitean random matrix ensemble of symplectic symmetry is given in terms of a quaternion determinant. Spectral properties of Gaussian ensembles are…
This paper addresses the asymptotic behavior of a particular type of information-plus-noise-type matrices, where the column and row number of the matrices are large and of the same order, while signals are diverged and time delays of the…
Using random matrix technique we determine an exact relation between the eigenvalue spectrum of the covariance matrix and of its estimator. This relation can be used in practice to compute eigenvalue invariants of the covariance…
The study of correlated time-series is ubiquitous in statistical analysis, and the matrix decomposition of the cross-correlations between time series is a universal tool to extract the principal patterns of behavior in a wide range of…
The properties of the first (largest) eigenvalue and its eigenvector (first eigenvector) are investigated for large sparse random symmetric matrices that are characterized by bimodal degree distributions. In principle, one should be able to…
Statistics derived from the eigenvalues of sample covariance matrices are called spectral statistics, and they play a central role in multivariate testing. Although bootstrap methods are an established approach to approximating the laws of…
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…
These expository notes serve as a reference for an accompanying post Morales-Jimenez et al. [2018]. In the spiked covariance model, we develop results on asymptotic normality of sample leading eigenvalues and certain projections of 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 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 use random matrix theory to study the spectrum of random geometric graphs, a fundamental model of spatial networks. Considering ensembles of random geometric graphs we look at short range correlations in the level spacings of the…
Using the Coulomb Fluid method, this paper derives central limit theorems (CLTs) for linear spectral statistics of three "spiked" Hermitian random matrix ensembles. These include Johnstone's spiked model (i.e., central Wishart with spiked…
We investigate random density matrices obtained by partial tracing larger random pure states. We show that there is a strong connection between these random density matrices and the Wishart ensemble of random matrix theory. We provide…