Related papers: On singular value distribution of large dimensiona…

In this article we investigate high-dimensional banded sample covariance matrices under the regime that the sample size $n$, the dimension $p$ and the bandwidth $d$ tend simultaneously to infinity such that $$n/p\to 0 \ \ \text{and} \ \…

This paper is concerned with the asymptotic empirical eigenvalue distribution of a non linear random matrix ensemble. More precisely we consider $M= \frac{1}{m} YY^*$ with $Y=f(WX)$ where $W$ and $X$ are random rectangular matrices with…

For two lacunary sequences $(M_{n,1})_{n\geq 2},(M_{n,2})_{n\geq 0}$ and suitable functions $f$ we introduce random matrix ensembles with \begin{equation*} X_{n,n'}=f(M_{n+n',1}x_1,M_{|n-n'|,2}x_2). \end{equation*} We prove weak convergence…

We consider the joint density distribution of the elements of certain random matrix models which are example of globally correlated and asymptotically scale-invariant distributions. It is shown that in their cases, the nonadditive entropy…

In this paper, we investigate the spectral properties of the sample canonical correlation (SCC) matrix under the alternative hypothesis to provide a more comprehensive description of the association between two sets of variables. Our…

Consider the ensemble of real symmetric Toeplitz matrices whose entries are i.i.d random variables chosen from a fixed probability distribution p of mean 0, variance 1 and finite higher moments. Previous work [BDJ,HM] showed that the…

We study the singularity probability of n*n random matrices with i.i.d. entries from highly biased discrete distributions. We obtain sharp non-asymptotic bounds for this probability and derive estimates on the least singular values. Our…

We investigate joint spectral characteristics of a family of matrices $\mathcal F $, associated with products in the semigroup generated by $\mathcal F$. In the literature, extremal measures such as the well-known joint spectral radius and…

We derive the universality principle for empirical spectral distributions of sample covariance matrices and their Stieltjes transforms. This principle states the following. Suppose quadratic forms of random vectors $y_p$ in $R^p$ satisfy a…

We study the spectral properties of a class of random matrices where the matrix elements depend exponentially on the distance between uniformly and randomly distributed points. This model arises naturally in various physical contexts, such…

Exact evaluation of $<{\rm Tr} S^p>$ is here performed for real symmetric matrices $S$ of arbitrary order $n$, up to some integer $p$, where the matrix entries are independent identically distributed random variables, with an arbitrary…

Planar N=4 Super Yang-Mills theory appears to be a quantum integrable four-dimensional conformal theory. This has been used to find equations believed to describe its exact spectrum of anomalous dimensions. Integrability seemingly also…

The "large p, small n" paradigm arises in microarray studies, where expression levels of thousands of genes are monitored for a small number of subjects. There has been an increasing demand for study of asymptotics for the various…

Let $x$ and $y$ be positive $n$-vectors. We show that there exists a $2n\times 2n$ positive definite real matrix whose symplectic spectrum is $y,$ and the symplectic spectrum of whose diagonal is $x$ if and only if $x$ is weakly…

For a pair of coupled rectangular random matrices we consider the squared singular values of their product, which form a determinantal point process. We show that the limiting mean distribution of these squared singular values is described…

Appropriately normalized square random Vandermonde matrices based on independent random variables with uniform distribution on the unit circle are studied. It is shown that as the matrix sizes increases without bound, with respect to the…

In this paper, we study the empirical spectral distribution of Spearman's rank correlation matrices, under the assumption that the observations are independent and identically distributed random vectors and the features are correlated. We…

We consider a dilute version of the Wigner ensemble of n-dimensional random matrices H such that each row has in average \rho_n non-zero elements. We study asymptotic properties of the spectral norm of H on the scale n^{-2/3} in the limit…

In this paper, the asymptotics of the spectral data (eigenvalues and weight numbers) are obtained for the higher-order differential operators with distribution coefficients and separated boundary conditions. Additionally, we consider the…

In this paper, we study inference for high-dimensional data characterized by small sample sizes relative to the dimension of the data. In particular, we provide an infinite-dimensional framework to study statistical models that involve…