Related papers: Isotropic covariance matrix functions on compact t…

We review and study some of the properties of smooth Gaussian random fields defined on a homogeneous space, under the assumption that the probability distribution is invariant under the isometry group of the space. We first give an…

Any symmetric affinity function $w: V\times V \to \mathbb{R}_+$ defined on a discrete set $V$ induces Euclidean space structure on $V$. In particular, an undirected graph specified by an affinity (or adjacency) matrix can be considered as a…

For stationary light fields, manifestation of statistical properties such as coherence and polarization are attributed to the same physical phenomena, i.e. correlations in fluctuations of optical fields. In order to explain various…

We consider the Itzykson-Zuber-Eynard-Mehta two-matrix model and prove that the partition function is an isomonodromic tau function in a sense that generalizes Jimbo-Miwa-Ueno's. In order to achieve the generalization we need to define a…

We summarize properties of the spatial sign covariance matrix and especially look at the relationship between its eigenvalues and those of the shape matrix of an elliptical distribution. The explicit relationship known in the bivariate case…

For warped products with harmonic curvature, nonconstant warping functions $\phi$, and compact two-dimensional bases $(M,h)$, we establish a dichotomy: either the Gaussian curvature $K$ of the metric $g=\phi^{-2}h$ is constant and negative,…

This paper introduces a new modeling framework for the statistical analysis of point patterns on a manifold M_{d}, defined by a connected and compact two-point homogeneous space, including the special case of the sphere. The presented…

We introduce a simple representation for isotropic spherical random fields and we discuss how it allows to discuss different notions of sparsity under isotropy. We also show how a suitable construction of sparse fields can mimic well the…

Let $(A_x)_{x\in\mathbb{R}^d}$ be a locally integrable, centered, weakly stationary random field, i.e. $\mathbb{E}[A_x]=0$, ${\rm Cov}(A_x,A_y)=K(x-y)$, $\forall x,y\in\mathbb{R}^d$, with measurable covariance function…

In this paper, the theory of functions of one complex variable is explored to study linearly full unramified holomorphic two-spheres with constant curvature in $G(2,n)$ satisfying that the generated harmonic sequence degenerates at position…

The standard estimator for the two-point function of a homogeneous and isotropic random field is a special case of a larger class of least squares estimators that interpolate the function values. Using a different interpolation scheme,…

This article introduces a method for estimating the smoothness of a stationary, isotropic Gaussian random field from irregularly spaced data. This involves novel constructions of higher-order quadratic variations and the establishment of…

We describe a statistical model to estimate the covariance matrix of matter tracer two-point correlation functions with cosmological simulations. Assuming a fixed number of cosmological simulation runs, we describe how to build a…

Context: Statistical properties of the cosmic density fields are to a large extent encoded in the shape of the one-point density probability distribution functions (PDF). In order to successfully exploit such observables, a detailed…

Through exploring the embedded transnormal systems of codimension 1, we show the existence of a transnormal function on a connected complete Riemannian manifold requires the underlying manifold to have a vector bundle structure or a linear…

In this paper we initiate the study of equivariant wave maps from 2d hyperbolic space into rotationally symmetric surfaces. This problem exhibits markedly different phenomena than its Euclidean counterpart due to the exponential volume…

We define a new class of Gaussian processes on compact metric graphs such as street or river networks. The proposed models, the Whittle--Mat\'ern fields, are defined via a fractional stochastic differential equation on the compact metric…

This paper considers homogeneous order preserving continuous maps on the normal cone of an ordered normed vector space. It is shown that certain operators of that kind which are not necessarily compact themselves but have a compact power…

Given a smooth foliation by complex curves (locally around a point $x\in\mathbb{C}^2\setminus\{0\}$) which is "compatible" with the foliation by spheres centered at the origin, we construct a smooth real-valued function $g$ in a…

Let $Z$ be a Boolean model based on a stationary Poisson process $\eta$ of compact, convex particles in Euclidean space ${\mathbb{R}}^d$. Let $W$ denote a compact, convex observation window. For a large class of functionals $\psi$, formulas…