Related papers: Limiting Spectral Distribution of Block Matrices w…

Spatial-sign covariance matrix (SSCM) is an important substitute of sample covariance matrix (SCM) in robust statistics. This paper investigates the SSCM on its asymptotic spectral behaviors under high-dimensional elliptical populations,…

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 consider inhomogeneous square random matrices of size $N$ with independent entries of mean 0 and finite variance. We assume that the variance profile of this matrix is doubly stochastic and has a band-like structure with an appropriately…

In this note, we give a precise description of the limiting empirical spectral distribution (ESD) for the non-backtracking matrices for an Erd\H{o}s-R\'{e}nyi graph assuming $np/\log n$ tends to infinity. We show that derandomizing part of…

Suppose $X_p$ is a real $p \times n$ matrix with independent entries and consider the (unscaled) sample covariance matrix $S_p=X_pX_p^T$. The Marchenko-Pastur law was discovered as the limit of the bulk distribution of the sample covariance…

We analyze the asymptotic fluctuations of linear eigenvalue statistics of random centrosymmetric matrices with i.i.d. entries. We prove that for a complex analytic test function, the centered and normalized linear eigenvalue statistics of…

We consider the eigenvalues of a fixed, non-normal matrix subject to a small additive perturbation. In particular, we consider the case when the fixed matrix is a banded Toeplitz matrix, where the bandwidth is allowed to grow slowly with…

Let $X$ be a matrix sampled uniformly from the set of doubly stochastic matrices of size $n\times n$. We show that the empirical spectral distribution of the normalized matrix $\sqrt{n}(X-{\mathbf {E}}X)$ converges almost surely to the…

Consider the product of $m$ independent $n\times n$ random matrices from the spherical ensemble for $m\ge 1$. The spectral radius is defined as the maximum absolute value of the $n$ eigenvalues of the product matrix. When $m=1$, the…

We consider random Hermitian matrices with independent upper triangular entries. Wigner's semicircle law says that under certain additional assumptions, the empirical spectral distribution converges to the semicircle distribution. We…

In this paper, we study the convergence rates of empirical spectral distribution of large dimensional quaternion sample covariance matrix. Assume that the entries of $\mathbf X_n$ ($p\times n$) are independent quaternion random variables…

In this article, we derive concentration inequalities for the spectral norm of two classical sample estimators of large dimensional Toeplitz covariance matrices, demonstrating in particular their asymptotic almost sure consistence. The…

The spectral moments of ensembles of sparse random block matrices are analytically evaluated in the limit of large order. The structure of the sparse matrix corresponds to the Erd\"os-Renyi random graph. The blocks are i.i.d. random…

Let $\a$ be a complex random variable with mean zero and bounded variance $\sigma^{2}$. Let $N_{n}$ be a random matrix of order $n$ with entries being i.i.d. copies of $\a$. Let $\lambda_{1}, ..., \lambda_{n}$ be the eigenvalues of…

We study the asymptotic distributions of the spiked eigenvalues and the largest nonspiked eigenvalue of the sample covariance matrix under a general covariance matrix model with divergent spiked eigenvalues, while the other eigenvalues are…

In several applications, one must estimate a real-valued (symmetric) Toeplitz covariance matrix, typically shifted by the conjugated diagonal matrices of phase progression and phase "calibration" errors. Unlike the Hermitian Toeplitz…

We show that the spectral radius of an $N\times N$ random symmetric matrix with i.i.d. bounded centered but non-symmetrically distributed entries is bounded from below by $ 2 \*\sigma - o(N^{-6/11+\epsilon}), $ where $\sigma^2 $ is the…

In this work we study the convergence properties of the one-level parallel Schwarz method with Robin transmission conditions applied to the one-dimensional and two-dimensional Helmholtz and Maxwell's equations. One-level methods are not…

We prove the circular law for a class of non-Hermitian random block band matrices with genuinely sublinear bandwidth. Namely, we show there exists $\tau \in (0,1)$ so that if the bandwidth of the matrix $X$ is at least $n^{1-\tau}$ and the…

Let $\mathbf{a}_{ij}$, $1\leq i\leq j\leq n$, be independent random variables and $\mathbf{a}_{ji}=\mathbf{a}_{ij}$, for all $i,j$. Suppose that every $\mathbf{a}_{ij}$ is bounded, has zero mean, and its variance is given by…