Related papers: Singular vector distribution of sample covariance …

We are concerned with the general problem of proving the existence of joint distributions of two discrete random variables $M$ and $N$ subject to infinitely many constraints of the form $\mathbb{P}\left(M=i,N=j\right)=0$. In particular, the…

An elliptic random matrix $X$ is a square matrix whose $(i,j)$-entry $X_{ij}$ is independent of the rest of the entries except possibly $X_{ji}$. Elliptic random matrices generalize Wigner matrices and non-Hermitian random matrices with…

The singular values squared of the random matrix product $Y = G_r G_{r-1} \cdots G_1 (G_0 + A)$, where each $G_j$ is a rectangular standard complex Gaussian matrix while $A$ is non-random, are shown to be a determinantal point process with…

We study the universality of the local eigenvalue statistics of Gaussian divisible Hermitian Wigner matrices. These random matrices are obtained by adding an independent GUE matrix to an Hermitian random matrix with independent elements, a…

For random matrix ensembles with non-gaussian matrix elements that may exhibit some correlations, it is shown that centered traces of polynomials in the matrix converge in distribution to a Gaussian process whose covariance matrix is…

In this paper, we study the subgaussian matrix variate model, where we observe the matrix variate data $X$ which consists of a signal matrix $X_0$ and a noise matrix $W$. More specifically, we study a subgaussian model using the Kronecker…

Following S\"odergren, we consider a collection of random variables on the space $X_n$ of unimodular lattices in dimension $n$: Normalizations of the angles between the $N = N(n)$ shortest vectors in a random unimodular lattice, and the…

Weak convergence of joint distributions generally does not imply convergence of conditional distributions. In particular, conditional distributions need not converge when joint Gaussian distributions converge to a singular Gaussian limit.…

We introduce a class of separable sample covariance matrices of the form $\widetilde{\mathcal{Q}}_1:=\widetilde A^{1/2} X \widetilde B X^* \widetilde A^{1/2}.$ Here $\widetilde{A}$ and $\widetilde{B}$ are positive definite matrices whose…

We consider two classical ensembles of the random matrix theory: the Wigner matrices and sample covariance matrices, and prove Central Limit Theorem for linear eigenvalue statistics under rather weak (comparing with results known before)…

Let $A\in\mathbb{R}^{m\times n}$ be a matrix of rank $r$ with singular value decomposition (SVD) $A=\sum_{k=1}^r\sigma_k (u_k\otimes v_k),$ where $\{\sigma_k, k=1,\ldots,r\}$ are singular values of $A$ (arranged in a non-increasing order)…

We give necessary and sufficient conditions to characterize the convergence in distribution of a sequence of arbitrary random variables to a probability distribution which is the invariant measure of a diffusion process. This class of…

We consider real, Gauss-divisible matrices $A_{t}=A+\sqrt{t}B$, where $B$ is from the real Ginibre ensemble. We prove that the bulk correlation functions converge to a universal limit for $t=O(N^{-1/3+\epsilon})$ if $A$ satisfies certain…

We prove the existence of the limiting spectral distribution (LSD) of symmetric triangular patterned matrices and also establish the joint convergence of sequences of such matrices. For the particular case of the symmetric triangular Wigner…

We consider a random matrix whose entries are independent Gaussian variables taking values in the field of quaternions with variance $1/n$. Using logarithmic potential theory, we prove the almost sure convergence, as the dimension $n$ goes…

Consider a deterministic self-adjoint matrix X_n with spectral measure converging to a compactly supported probability measure, the largest and smallest eigenvalues converging to the edges of the limiting measure. We perturb this matrix by…

We study the largest eigenvalue of a Gaussian random symmetric matrix $X_n$, with zero-mean, unit variance entries satisfying the condition $\sup_{(i, j) \ne (i', j')}|\mathbb{E}[X_{ij} X_{i'j'}]| = O(n^{-(1 + \varepsilon)})$, where…

We present a Gaussian ensemble of random cyclic matrices on the real field and study their spectral fluctuations. These cyclic matrices are shown to be pseudo-symmetric with respect to generalized parity. We calculate the joint probability…

The Singular Value Decomposition is a matrix decomposition technique widely used in the analysis of multivariate data, such as complex space-time images obtained in both physical and biological systems. In this paper, we examine the…

Pencils of Hankel matrices whose elements have a joint Gaussian distribution with nonzero mean and not identical covariance are considered. An approximation to the distribution of the squared modulus of their determinant is computed which…