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Existence of Gibbsian point processes with geometry-dependent interactions
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In this article, the authors established the existence of stationary Gibbsian point processes for interactions that act on hyperedges between the points, such as Delaunay edges or triangles, cliques of Voronoi cells or clusters of $k$-nearest neighbors.Abstract:
We establish the existence of stationary Gibbsian point processes for interactions that act on hyperedges between the points. For example, such interactions can depend on Delaunay edges or triangles, cliques of Voronoi cells or clusters of $k$-nearest neighbors. The classical case of pair interactions is also included. The basic tools are an entropy bound and stationarity.read more
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Book ChapterDOI
Introduction to the theory of Gibbs point processes
TL;DR: In this article, the existence, uniqueness and non-uniqueness of Gibbs point processes (GPPs) are investigated with completely self-contained proofs, and the DLR equations, the GNZ equations and the variational principle are presented as well.
Journal ArticleDOI
Logistic regression for spatial Gibbs point processes
TL;DR: This work proposes a computationally efficient technique, based on logistic regression, for fitting Gibbs point process models to spatial point pattern data and proves that the parameter estimator is strongly consistent and asymptotically normal, and proposes a variance estimator.
Journal ArticleDOI
A tutorial on Palm distributions for spatial point processes
TL;DR: In this paper, the authors provide an introduction to Palm distributions for spatial point processes and discuss some examples of Palm distribution for specific models and some applications, and give an explicit definition of Palm distributions in terms of their density functions.
Journal ArticleDOI
Fast Covariance Estimation for Innovations Computed from a Spatial Gibbs Point Process
TL;DR: In this paper, an exact formula for the covariance of two innovations computed from a spatial Gibbs point process was derived and a fast method for estimating this covariance was proposed. But this method is not suitable for the analysis of point patterns.
References
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Book
Statistical Mechanics: Rigorous Results
TL;DR: The problem of phase transition group invariance of physical states has been studied in the literature as discussed by the authors, where the thermodynamic limit for thermodynamic functions has been investigated in the context of statistical mechanics.
Book
Gibbs Measures and Phase Transitions
TL;DR: This comprehensive monograph covers in depth a broad range of topics in the mathematical theory of phase transition in statistical mechanics and serves both as an introductory text and as a reference for the expert.
Journal ArticleDOI
The Influence of Cell Mechanics, Cell-Cell Interactions, and Proliferation on Epithelial Packing
TL;DR: A vertex model is used for the epithelial junctional network in which cell packing geometries correspond to stable and stationary network configurations and accounts qualitatively and quantitatively for the observed packing geometry in the wing disc and its response to perturbation by laser ablation.
Book
Stochastic and Integral Geometry
Rolf Schneider,Wolfgang Weil +1 more
TL;DR: This chapter discusses the foundations of Stochastic Geometry, as well as some Geometric Probability Problems, and some of the facts from Convex Geometry.
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