Lectures on random Voronoi tessellations
From MaRDI portal
Publication:1326796
zbMath0812.60016MaRDI QIDQ1326796
Publication date: 14 June 1994
Published in: Lecture Notes in Statistics (Search for Journal in Brave)
mosaictessellationpoint processspatial point processesnon-random properties of Voronoi tessellationsPoisson-Voronoi tessellations
Geometric probability and stochastic geometry (60D05) Point processes (e.g., Poisson, Cox, Hawkes processes) (60G55) Research exposition (monographs, survey articles) pertaining to probability theory (60-02)
Related Items (86)
Cell Shape Analysis of Random Tessellations Based on Minkowski Tensors ⋮ Asymptotics for Voronoi tessellations on random samples ⋮ Criteria for Poisson process convergence with applications to inhomogeneous Poisson-Voronoi tessellations ⋮ Phase transitions in Delaunay Potts models ⋮ Subcritical regimes in some models of continuum percolation ⋮ Continuum percolation in high dimensions ⋮ The -Delaunay tessellation: Description of the model and geometry of typical cells ⋮ Statistical properties of Poisson-Voronoi tessellation cells in bounded regions ⋮ Approximations of functionals of some modulated-Poisson Voronoi tessellations with applications to modeling of communication networks ⋮ Pair correlation functions and limiting distributions of iterated cluster point processes ⋮ On the Volume of the Zero Cell of a Class of Isotropic Poisson Hyperplane Tessellations ⋮ Multitype threshold growth: Convergence to Poisson-Voronoi tessellations ⋮ Distance from the nucleus to a uniformly random point in the 0-cell and the typical cell of the Poisson-Voronoi tessellation ⋮ Asymptotic Methods for Random Tessellations ⋮ The typical cell of a Voronoi tessellation on the sphere ⋮ On the approximation of mean densities of random closed sets ⋮ Some new classes of stationary max-stable random fields ⋮ Unnamed Item ⋮ On estimation of the intensity function of a point process ⋮ A Tutorial on Palm Distributions for Spatial Point Processes ⋮ A full characterization of invariant embeddability of unimodular planar graphs ⋮ Nonparametric estimation of surface integrals ⋮ Power diagrams and interaction processes for unions of discs ⋮ Connected spatial networks over random points and a route-length statistic ⋮ A numerical method for the generation of hierarchical Poisson Voronoi microstructures applied in micromechanical finite element simulations. I: Method ⋮ Faces of Poisson-Voronoi mosaics ⋮ Practical simulation and estimation for Gibbs Delaunay-Voronoi tessellations with geometric hardcore interaction ⋮ Random Laguerre tessellations ⋮ The Poisson-Voronoi tessellation: relationships for edges ⋮ Angles of random simplices and face numbers of random polytopes ⋮ Recursive scheme for angles of random simplices, and applications to random polytopes ⋮ Extreme values for characteristic radii of a Poisson-Voronoi tessellation ⋮ Stochastic geometric models, and related statistical issues in tumour-induced angiogenesis ⋮ Asymptotic statistics of then-sided planar Poisson–Voronoi cell: II. Heuristics ⋮ Planar discrete birth-growth Poisson–Voronoi tessellations with the von Neumann neighbourhood ⋮ Subcritical regimes in the Poisson Boolean model of continuum percolation ⋮ Stochastic geometry and related statistical problems in biomedicine ⋮ Point processes in general position ⋮ Gamma distributions for stationary Poisson flat processes ⋮ Set Reconstruction by Voronoi Cells ⋮ Exponential moments for planar tessellations ⋮ Limit theorems for functionals on the facets of stationary random tessellations ⋮ A Formula for the Edge Length Distribution Function of the Poisson Voronoi Tessellation ⋮ Median-based estimation of the intensity of a spatial point process ⋮ Probabilistic results for a mobile service scenario ⋮ Random line tessellations of the plane: Statistical properties of many-sided cells ⋮ The Poisson Voronoi Tessellation III. Miles' Formula ⋮ On variances of partial volumes of the typical cell of a Poisson-Voronoi tessellation and large-dimensional volume degeneracy ⋮ The second volume moment of the typical cell and higher moments of edge lengths of the spatial Poisson-Voronoi tessellation ⋮ Large Poisson-Voronoi cells and Crofton cells ⋮ Voronoi random field and its application to the fuzzy post office problem ⋮ Statistical and renewal results for the random sequential adsorption model applied to a unidirectional multicracking problem ⋮ Simultaneous closeness among order statistics to population quantiles ⋮ A microscopic probabilistic description of a locally regulated population and macroscopic approximations ⋮ Bernoulli cluster field: Voronoi tessellations. ⋮ The palm measure and the Voronoi tessellation for the Ginibre process ⋮ Empirical means for the Voronoi tessellations of the Poincaré disc. ⋮ Integral representation results for energies defined on stochastic lattices and application to nonlinear elasticity ⋮ Volume degeneracy of the typical cell and the chord length distribution for Poisson-Voronoi tessellations in high dimensions ⋮ On the correlation between the volumes of the typical Poisson-Voronoi cell and the typical Stienen sphere ⋮ On the measure of Voronoi cells ⋮ The Widom-rowlinson model on the Delaunay graph ⋮ Central limit theorems for Poisson hyperplane tessellations ⋮ A general study of extremes of stationary tessellations with examples ⋮ Derivation of Darcy's law in randomly perforated domains ⋮ Recurrence or transience of random walks on random graphs generated by point processes in \(\mathbb{R}^d\) ⋮ A geometric model for coarsening during spiral-mode growth of thin films ⋮ Functional summary statistics for the Johnson–Mehl model ⋮ From statistical polymer physics to nonlinear elasticity ⋮ An explicit expression for the distribution of the number of sides of the typical Poisson-Voronoi cell ⋮ Poisson-Voronoi approximation ⋮ Precise formulae for the distributions of the principal geometric characteristics of the typical cells of a two-dimensional Poisson-Voronoi tessellation and a Poisson line process ⋮ Criticality and covered area fraction in confetti and Voronoi percolation ⋮ Poisson approximation with applications to stochastic geometry ⋮ Large planar Poisson-Voronoi cells containing a given convex body ⋮ Equivalence of some subcritical properties in continuum percolation ⋮ Fractal random series generated by Poisson-Voronoi tessellations ⋮ Quasicrystals and almost periodicity ⋮ Limit theorems for the typical Poisson-Voronoi cell and the Crofton cell with a large inradius ⋮ Asymptotic properties of random Voronoi cells with arbitrary underlying density ⋮ Some distributional results for Poisson-Voronoi tessellations ⋮ Unnamed Item ⋮ The law of the smallest disk containing the typical Poisson-Voronoi cell ⋮ Continuum line-of-sight percolation on Poisson–Voronoi tessellations ⋮ A Sequential Point Process Model and Bayesian Inference for Spatial Point Patterns with Linear Structures ⋮ Diffraction and Palm measure of point processes
This page was built for publication: Lectures on random Voronoi tessellations
