Related papers: Structured space-sphere point processes and $K$-fu…
We study point processes on $\mathbb S^d$, the $d$-dimensional unit sphere $\mathbb S^d$, considering both the isotropic and the anisotropic case, and focusing mostly on the spherical case $d=2$. The first part studies reduced Palm…
We study special functions on euclidean spaces from the viewpoint of riemannian symmetric spaces. Here the euclidean space $E^n = G/K$ where $G$ is the semidirect product $R^n \cdot K$ of the translation group with a closed subgroup $K$ of…
Analysis of images of sets of fibers such as myelin sheaths or skeletal muscles must account for both the spatial distribution of fibers and differences in fiber shape. This necessitates a combination of point process and shape analysis…
It is well known that one can map certain properties of random matrices, fermionic gases, and zeros of the Riemann zeta function to a unique point process on the real line. Here we analytically provide exact generalizations of such a point…
Motivated by the study of an important data set for understanding the large-scale structure of the universe, this work considers the estimation of the reduced second moment function, or K-function, of a stationary point process observed…
After reviewing the basic relevant properties of stationary stochastic processes (SSP), defining basic terms and quantities, we discuss the properties of the so-called Harrison-Zeldovich like spectra. These correlations, usually…
There is a growing interest in developing covariance functions for processes on the surface of a sphere due to wide availability of data on the globe. Utilizing the one-to-one mapping between the Euclidean distance and the great circle…
In this paper, we describe the irreducible spherical functions of fundamental $K$-types associated with the pair $(G,K)=({\mathrm{SO}}(n+1),{\mathrm{SO}}(n))$ in terms of matrix hypergeometric functions. The output of this description is…
The fundamental functional summary statistics used for studying spatial point patterns are developed for marked homogeneous and inhomogeneous point processes on the surface of a sphere. These are extended to point processes on the surface…
The K function and its related statistics have been an enduring tool in the analysis of spatial point processes, providing an easy to compute and interpret summary statistic for characterising the interactions between points of one type, or…
The classification of solutions to semilinear partial differential equations, as well as the classification of critical points of the corresponding functionals, have wide applications in the study of partial differential equations and…
This paper establishes the theoretical foundation for statistical applications of an intriguing new type of spatial point processes called critical point processes. These point processes, residing in Euclidean space, consist of the critical…
The goal of this paper is to quantitatively describe some statistical properties of higher-dimensional determinantal point processes with a primary focus on the nearest-neighbor distribution functions. Toward this end, we express these…
We propose a new summary statistic for inhomogeneous intensity-reweighted moment stationary spatio-temporal point processes. The statistic is defined through the n-point correlation functions of the point process and it generalises the…
The $K$-function is arguably the most important functional summary statistic for spatial point processes. It is used extensively for goodness-of-fit testing and in connection with minimum contrast estimation for parametric spatial point…
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…
After reviewing some basic relevant properties of stationary stochastic processes (SSP), we discuss the properties of the so-called Harrison-Zeldovich like spectra of mass density perturbations. These correlations are a fundamental feature…
U-statistics of spatial point processes given by a density with respect to a Poisson process are investigated. In the first half of the paper general relations are derived for the moments of the functionals using kernels from the Wiener-Ito…
In this paper we establish a close relationship between the spherical functions of the $n$-dimensional sphere $S^n\simeq\SO(n+1)/\SO(n)$ and the spherical functions of the $n$-dimensional real projective space…
This paper introduces a $K$-function for assessing second-order properties of inhomogeneous random measures generated by marked point processes. The marks can be geometric objects like fibers or sets of positive volume, and the presented…