Related papers: Gilbert's disc model with geostatistical marking
A class of 2x2 random-matrix models is introduced for which the Brody distribution is the exact eigenvalue spacing distribution. The matrix elements consist of constrained finite sums of an exponential random variable raised to various…
Following our earlier work, we construct statistical discrete geometry by applying statistical mechanics to discrete (Regge) gravity. We propose a coarse-graining method for discrete geometry under the assumptions of atomism and background…
Geostatistical modeling for continuous point-referenced data has been extensively applied to neuroimaging because it produces efficient and valid statistical inference. However, diffusion tensor imaging (DTI), a neuroimaging characterizing…
We study a family of parametric statistical models based on gamma distributions, which do give realistic descriptions for other stochastic porous media. Gamma distributions contain as a special case the exponential distributions, which…
This paper presents a new approach to the estimation of the deformation of an isotropic Gaussian random field on $\mathbb{R}^2$ based on dense observations of a single realization of the deformed random field. Under this framework we…
In this article, we consider a configuration of weighted random balls in $\mathbb{R}^d$ generated according to a Poisson point process. The model investigated exhibits inhomogeneity, as well as dependence between the centers and the radii…
We develop a technique to estimate spatially varying seismicity patterns. It is based on a Gaussian approximation of the underlying Poisson Process. A link function is used to estimate local moments of the seismicity from observed…
We discuss recent results of the replica approach to statistical mechanics of a single classical particle placed in a random N(>>1)-dimensional Gaussian landscape. The particular attention is paid to the case of landscapes with…
In modeling spatial processes, a second-order stationarity assumption is often made. However, for spatial data observed on a vast domain, the covariance function often varies over space, leading to a heterogeneous spatial dependence…
Define the scale-free Gilbert graph based on a Boolean model with heavy-tailed radius distribution on the $d$-dimensional torus by connecting two centers of balls by an edge if at least one of the balls contains the center of the other. We…
In this paper, we study the generation of maximal Poisson-disk sets with varying radii. First, we present a geometric analysis of gaps in such disk sets. This analysis is the basis for maximal and adaptive sampling in Euclidean space and on…
This paper introduces a new stochastic process with values in the set Z of integers with sign. The increments of process are Poisson differences and the dynamics has an autoregressive structure. We study the properties of the process and…
We consider stationary configurations of points in Euclidean space which are marked by positive random variables called scores. The scores are allowed to depend on the relative positions of other points and outside sources of randomness.…
A new two-parameter discrete distribution, namely the PoiG distribution is derived by the convolution of a Poisson variate and an independently distributed geometric random variable. This distribution generalizes both the Poisson and…
We consider a continuous-time random walk which is the generalization, by means of the introduction of waiting periods on sites, of the one-dimensional nonhomogeneous random walk with a position-dependent drift known in the mathematical…
A Poisson outdegree-one graph is an oriented graph based on a Poisson point process such that each vertex has only one outgoing edge. The paper focuses on the absence of percolation for such graphs. Our main result is based on two…
We derive for generally covariant theories the generic dependency of observables on the original fields, corresponding to coordinate-dependent gauge fixings. This gauge choice is equivalent to a choice of intrinsically defined coordinates…
We study random perturbations of Riemannian manifolds $(\mathsf{M},\mathsf{g})$ by means of so-called Fractional Gaussian Fields, which are defined intrinsically by the given manifold. The fields $h^\bullet: \omega\mapsto h^\omega$ will act…
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…
Stationary Random Functions have been successfully applied in geostatistical applications for decades. In some instances, the assumption of a homogeneous spatial dependence structure across the entire domain of interest is unrealistic. A…