相关论文: Covariance matrices of self-affine measures

We derive analytical shape derivative formulas of the system matrix representing electric field integral equation discretized with Raviart-Thomas basis functions. The arising integrals are easy to compute with similar methods as the entries…

We shall present an elementary approach to extremal decompositions of (quantum) covariance matrices determined by densities. We give a new proof on former results and provide a sharp estimate of the ranks of the densities that appear in the…

In this paper, we solve the long standing open problem on exact dimensionality of self-affine measures on the plane. We show that every self-affine measure on the plane is exact dimensional regardless of the choice of the defining iterated…

New bounds are derived for the eigenvalues of sums of Kronecker products of square matrices by relating the corresponding matrix expressions to the covariance structure of suitable bi-linear stochastic systems in discrete and continuous…

The multiresolution analysis of Alpert is considered. Explicit formulas for the entries in the matrix coefficients of the refinement equation are given in terms of hypergeometric functions. These entries are shown to solve generalized…

In this paper, closed formulas for the eigenvectors of a particular class of matrices generated by generalized permutation matrices, named generalized circulant matrices, are presented.

We propose a general procedure for estimating the variance-covariance matrix of two-step estimates of structural parameters in latent variable models. The method is partially simulation-based, in that it includes drawing simulated values of…

When inferring parameters from a Gaussian-distributed data set by computing a likelihood, a covariance matrix is needed that describes the data errors and their correlations. If the covariance matrix is not known a priori, it may be…

In a previous paper [M.~Hanada, H.~Kawai and Y.~Kimura, Prog. Theor. Phys. 114 (2005), 1295] it is shown that a covariant derivative on any n-dimensional Riemannian manifold can be expressed in terms of a set of n matrices, and a new…

We establish a large deviation theorem for the empirical spectral distribution of random covariance matrices whose entries are independent random variables with mean 0, variance 1 and having controlled forth moments. Some new properties of…

We consider small factor analysis models with one or two factors. Fixing the number of factors, we prove a finiteness result about the covariance matrix parameter space when the size of the covariance matrix increases. According to this…

For convex univalent functions we give instances where the sharp bound for various coefficient functionals are identical to those for the corresponding bound for the inverse function. We give instances where the sharp bounds differ and also…

It has been proposed that complex populations, such as those that arise in genomics studies, may exhibit dependencies among observations as well as among variables. This gives rise to the challenging problem of analyzing unreplicated…

We consider a covariance matrix composed of asymmetric and free random Levy matrices. We use the results of free random variables to derive an algebraic equation for the resolvent and solve it to extract the spectral density. For an…

We derive concentration inequalities for functions of the empirical measure of large random matrices with infinitely divisible entries and, in particular, stable ones. We also give concentration results for some other functionals of these…

We show that any affine invariant function on the set of positive definite matrices must factor through the determinant function, as long as the restriction of the function to scalar matrices is surjective. A motivation from robust…

We consider the problem of finding the Perron-Frobenius eigenvector of a primitive matrix. Dividing each of the rows of the matrix by the sum of the elements in the row, the resulting new matrix is stochastic. We give a formula for the…

This paper calculates the fluctuations of eigenvalues of polynomials on large Haar unitaries cut by finite rank deterministic matrices. When the eigenvalues are all simple, we can give a complete algorithm for computing the fluctuations.…

We introduce An(1) (n=1,2,...) affine quiver matrix model by simply adopting the extended Cartan matrices as incidence matrices and study its finite N Schwinger-Dyson equations as well as their planar limit. In the case of n=1, we extend…

Covariance matrices are essential cosmological probes of fundamental physics, providing information on numerous fundamental physical parameters and varying with any change in the underlying cosmology. However, this cosmology dependence,…