相关论文: Covariance matrices of volume power functionals of…

Asymptotic properties of a vector of length power functionals of random geometric graphs are investigated. More precisely, its asymptotic covariance matrix is studied as the intensity of the underlying homogeneous Poisson point process…

We investigate the high-dimensional asymptotic distributional behavior of the $\mathbf{f}$-vector of a random Vietoris-Rips complex, that is generated over a stationary Poisson point process in $[-\frac{1}{2}, \frac{1}{2}]^d$ as the space…

There has been considerable recent interest, primarily motivated by problems in applied algebraic topology, in the homology of random simplicial complexes. We consider the scenario in which the vertices of the simplices are the points of a…

We study the asymptotics of sums of matricially free random variables called random pseudomatrices, and we compare it with that of random matrices with block-identical variances. For objects of both types we find the limit joint…

We consider a $p$-dimensional time series where the dimension $p$ increases with the sample size $n$. The resulting data matrix $X$ follows a stochastic volatility model: each entry consists of a positive random volatility term multiplied…

Power law generalized covariance functions provide a simple model for describing the local behavior of an isotropic random field. This work seeks to extend this class of covariance functions to spatial-temporal processes for which the…

In this paper we define certain analogues of the volume of a divisor - called asymptotic cohomological functions - and investigate their behaviour on the Neron--Severi space. We establish that asymptotic cohomological functions are…

A general form of the covariance matrix function is derived in this paper for a vector random field that is isotropic and mean square continuous on a compact connected two-point homogeneous space and stationary on a temporal domain. A…

We study the partition function from random matrix theory using a well known connection to orthogonal polynomials, and a recently developed Riemann-Hilbert approach to the computation of detailed asymptotics for these orthogonal…

The problem of detecting changes in covariance for a single pair of features has been studied in some detail, but may be limited in importance or general applicability. In contrast, testing equality of covariance matrices of a {\it set} of…

In this paper we introduce a method which allows us to study properties of the random uniform simplicial complex. That is, we assign equal probability to all simplicial complexes with a given number of vertices and then consider properties…

The power spectrum and the voxel intensity distribution (VID) are two of the main proposed summary statistics to study line-intensity maps. We reformulate the derivation of the VID in terms of the local overdensities and derive for the…

We derive the asymptotic distribution of ordinal-pattern frequencies under weak dependence conditions and investigate the long-run covariance matrix not only analytically for moving-average, Gaussian, and the novel generalized coin-tossing…

We prove a number of results concerning the large $N$ asymptotics of the free energy of a random matrix model with a polynomial potential $V(z)$. Our approach is based on a deformation $\tau_tV(z)$ of $V(z)$ to $z^2$, $0\le t<\infty$ and on…

The intrinsic volumes induced by a stationary Poisson k-flat process inside a compact and convex sampling window are considered. Using techniques from stochastic analysis, more precisely calculus with multiple stochastic integrals and a…

This is a tutorial on some basic non-asymptotic methods and concepts in random matrix theory. The reader will learn several tools for the analysis of the extreme singular values of random matrices with independent rows or columns. Many of…

The covariance matrix function is characterized in this paper for a Gaussian or elliptically contoured vector random field that is stationary, isotropic, and mean square continuous on the compact two-point homogeneous space. Necessary and…

The association between two random variables is often of primary interest in statistical research. In this paper semiparametric models for the association between random vectors X and Y are considered which leave the marginal distributions…

Covariance parameter estimation of Gaussian processes is analyzed in an asymptotic framework. The spatial sampling is a randomly perturbed regular grid and its deviation from the perfect regular grid is controlled by a single scalar…

We show that the limiting variance of a sequence of estimators for a structured covariance matrix has a general form that appears as the variance of a scaled projection of a random matrix that is of radial type and a similar result is…