Extreme values for characteristic radii of a Poisson-Voronoi tessellation

DOI10.1007/s10687-014-0184-yzbMath1316.60021arXiv1304.0170OpenAlexW2000943710MaRDI QIDQ488103

Nicolas Chenavier, Pierre Calka

Publication date: 23 January 2015

Published in: Extremes (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1304.0170

zbMATH Keywords

boundary effectsPoisson point processextremesrandom covering of the sphereVoronoi tessellations

Mathematics Subject Classification ID

Geometric probability and stochastic geometry (60D05) Central limit and other weak theorems (60F05) Statistics of extreme values; tail inference (62G32) Random convex sets and integral geometry (aspects of convex geometry) (52A22)

Related Items

Criteria for Poisson process convergence with applications to inhomogeneous Poisson-Voronoi tessellations, Extremal linkage networks, Extremal lifetimes of persistent cycles, Cluster size distributions of extreme values for the Poisson-Voronoi tessellation, Poisson Point Process Convergence and Extreme Values in Stochastic Geometry, Poisson process approximation under stabilization and Palm coupling, Introduction to Stochastic Geometry, Large nearest neighbour balls in hyperbolic stochastic geometry, Random Euclidean coverage from within, Asymptotic distributions of covering and separation measures on the hypersphere, Boundary density and Voronoi set estimation for irregular sets, Random Point Sets on the Sphere—Hole Radii, Covering, and Separation, On the longest gap between power-rate arrivals, Planar discrete birth-growth Poisson–Voronoi tessellations with the von Neumann neighbourhood, The largest order statistics for the inradius in an isotropic STIT tessellation, The β-mixing rate of STIT tessellations, A general study of extremes of stationary tessellations with examples, The limit distribution of the maximum probability nearest-neighbour ball, Poisson approximation with applications to stochastic geometry, Poisson polyhedra in high dimensions

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The scaling limit of Poisson-driven order statistics with applications in geometric probability
• Storm processes and stochastic geometry
• Point processes in general position
• Limit theorems for diameter of a random sample in the unit ball
• Poisson-Voronoi approximation
• Random coverings in several dimensions
• Limit theorems for a triangular scheme of U-statistics with applications to inter-point distances
• Extreme value theory for dependent sequences via the Stein-Chen method of Poisson approximation
• Lectures on random Voronoi tessellations
• Poisson approximation and the Chen-Stein method. With comments and a rejoinder by the authors
• Stereology of extremes; shape factor of spheroids
• Foundations of quantization for probability distributions
• LOCAL STEREOLOGY OF EXTREMES
• Some distributional results for Poisson-Voronoi tessellations
• Stochastic and Integral Geometry
• On the Geometric Densities of Random Closed Sets
• The limit distribution for maxima of ‘weighted' rth-nearest-neighbour distances
• On the almost sure coverage property of Voronoi tessellation: the ℝ¹ case
• On a Voronoi aggregative process related to a bivariate Poisson process
• Random Geometric Graphs
• An explicit expression for the distribution of the number of sides of the typical Poisson-Voronoi cell
• Large Poisson-Voronoi cells and Crofton cells
• Limit theorems for stationary tessellations with random inner cell structures
• The distributions of the smallest disks containing the Poisson-Voronoi typical cell and the Crofton cell in the plane
• Random tessellations in ℝ^d
• Extremes and local dependence in stationary sequences
• Set Reconstruction by Voronoi Cells
• Stochastic Geometry and Wireless Networks: Volume II Applications
• Adaptive Finite Element Methods for Elliptic PDEs Based on Conforming Centroidal Voronoi–Delaunay Triangulations
• Second‐order properties of the point process of nodes in a stationary Voronoi tessellation
• Extreme Values in Uniformly Mixing Stationary Stochastic Processes
• On extreme values in stationary sequences
• The Poisson-Voronoi tessellation: relationships for edges