Related papers: Bulk behaviour of skew-symmetric patterned random …
The product of a complex skew-symmetric matrix and its conjugate transpose is a positive semi-definite Hermitian matrix with nonnegative eigenvalues, with a property that each distinct positive eigenvalue has even multiplicity. This…
High-dimensional sample correlation matrices are a crucial class of random matrices in multivariate statistical analysis. The central limit theorem (CLT) provides a theoretical foundation for statistical inference. In this paper, assuming…
The singular value and spectral distribution of Toeplitz matrix sequences with Lebesgue integrable generating functions is well studied. Early results were provided in the classical Szeg{\H{o}} theorem and the Avram-Parter theorem, in which…
Sine-skewed circular distributions are identifiable and have easily-computable trigonometric moments and a simple random number generation algorithm, whereas they are known to have relatively low levels of asymmetry. This study proposes a…
We consider symmetric and Hermitian random matrices whose entries are independent and symmetric random variables with an arbitrary variance pattern. Under a novel Short-to-Long Mixing condition, which is sharp in the sense that it precludes…
We prove large deviation principles (LDPs) for random matrices in the orthogonal group and Stiefel manifold, determining both the speed and good convex rate functions that are explicitly given in terms of certain log-determinants of…
We consider a discrete, non-Hermitian random matrix model, which can be expressed as a shift of a rank-one perturbation of an anti-symmetric matrix. We show that, asymptotically almost surely, the real parts of the eigenvalues of the…
For a large class of symmetric random matrices with correlated entries, selected from stationary random fields of centered and square integrable variables, we show that the limiting distribution of eigenvalue counting measure always exists…
This paper introduces constrained mixtures for continuous distributions, characterized by a mixture of distributions where each distribution has a shape similar to the base distribution and disjoint domains. This new concept is used to…
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 determine representatives for the mutation classes of skew-symmetrizable 3x3 matrices and associated graphs using a natural minimality condition, generalizing and strengthening results of Beineke-Brustle-Hille and…
Three-way data can be conveniently modelled by using matrix variate distributions. Although there has been a lot of work for the matrix variate normal distribution, there is little work in the area of matrix skew distributions. Three matrix…
We propose matrix norm inequalities that extend the Recht-R\'e (2012) conjecture on a noncommutative AM-GM inequality by supplementing it with another inequality that accounts for single-shuffle, which is a widely used without-replacement…
In this work, we study a class of random matrices which interpolate between the Wigner matrix model and various types of patterned random matrices such as random Toeplitz, Hankel, and circulant matrices. The interpolation mechanism is…
A linked system of symmetric designs (LSSD) is a $w$-partite graph ($w\geq 2$) where the incidence between any two parts corresponds to a symmetric design and the designs arising from three parts are related. The original construction for…
Consider real symmetric, complex Hermitian Toeplitz and real symmetric Hankel band matrix models, where the bandwidth $b_{N}\ra \iy$ but $b_{N}/N \to b$, $b\in [0,1]$ as $N\to \infty$. We prove that the distributions of eigenvalues converge…
We present a new approach, based on graphon theory, to finding the limiting spectral distributions of general Wigner-type matrices. This approach determines the moments of the limiting measures and the equations of their Stieltjes…
It is a classical result of Wigner that for an hermitian matrix with independent entries on and above the diagonal, the mean empirical eigenvalue distribution converges weakly to the semicircle law as matrix size tends to infinity. In this…
We estimate the norms of standard Gaussian random Toeplitz and circulant matrices and their inverses, mostly by means of combining some basic techniques of linear algebra. In the case of circulant matrices we obtain sharp probabilistic…
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…