Related papers: Random Matrices and U-Statistics

In this paper, we investigate the limiting spectral distribution of the sample correlation matrix, whose sample vectors are $k$-fold tensor products of $n$-dimensional vectors with i.i.d. entries. We focus on the limiting regime $n,k \to…

We present a general method to detect and extract from a finite time sample statistically meaningful correlations between input and output variables of large dimensionality. Our central result is derived from the theory of free random…

We prove a local law in the bulk of the spectrum for random Gram matrices $XX^*$, a generalization of sample covariance matrices, where $X$ is a large matrix with independent, centered entries with arbitrary variances. The limiting…

We determine the asymptotic distribution of the sum of correlated variables described by a matrix product ansatz with finite matrices, considering variables with finite variances. In cases when the correlation length is finite, the law of…

This paper studies the asymptotic spectral properties of the sample covariance matrix for high dimensional compositional data, including the limiting spectral distribution, the limit of extreme eigenvalues, and the central limit theorem for…

We study random matrices whose entries are obtained by applying consistent rank correlations, such as Hoeffding's $D$, pairwise to a high-dimensional random vector with mutually independent components. Prior work has shown that, in the…

We consider a class of real random matrices with dependent entries and show that the limiting empirical spectral distribution is given by the Marchenko-Pastur law. Additionally, we establish a rate of convergence of the expected empirical…

We study (asymmetric) $U$-statistics based on a stationary sequence of $m$-dependent variables; moreover, we consider constrained $U$-statistics, where the defining multiple sum only includes terms satisfying some restrictions on the gaps…

We study various methods to generate ensembles of random density matrices of a fixed size N, obtained by partial trace of pure states on composite systems. Structured ensembles of random pure states, invariant with respect to local unitary…

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.

We derive the Marchenko-Pastur (MP) law for sample covariance matrices of the form $V_n=\frac{1}{n}XX^T$, where $X$ is a $p\times n$ data matrix and $p/n\to y\in(0,\infty)$ as $n,p \to \infty$. We assume the data in $X$ stems from a…

We study high-dimensional sample covariance matrices based on independent random vectors with missing coordinates. The presence of missing observations is common in modern applications such as climate studies or gene expression…

Spectral correlations in unitary invariant, non-Gaussian ensembles of large random matrices possessing an eigenvalue gap are studied within the framework of the orthogonal polynomial technique. Both local and global characteristics of…

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…

For two large matrices ${\mathbf X}$ and ${\mathbf Y}$ with Gaussian i.i.d.\ entries and dimensions $T\times N_X$ and $T\times N_Y$, respectively, we derive the probability distribution of the singular values of $\mathbf{X}^T \mathbf{Y}$ in…

We consider matrix-valued processes described as solutions to stochastic differential equations of very general form. We study the family of the empirical measure-valued processes constructed from the corresponding eigenvalues. We show that…

We consider certain large random matrices, called random inner-product kernel matrices, which are essentially given by a nonlinear function $f$ applied entrywise to a sample-covariance matrix, $f(X^TX)$, where $X \in \mathbb{R}^{d \times…

Random matrix theory is used to assess the significance of weak correlations and is well established for Gaussian statistics. However, many complex systems, with stock markets as a prominent example, exhibit statistics with power-law tails,…

This paper studies the spectral behavior of large dimensional Chatterjee's rank correlation matrix when observations are independent draws from a high-dimensional random vector with independent continuous components. We show that the…

This paper investigates the spectral properties of spatial-sign covariance matrices, a self-normalized version of sample covariance matrices, for data from $\alpha$-regularly varying populations with general covariance structures. By…