Large Poisson-Voronoi cells and Crofton cells

DOI10.1239/aap/1093962228zbMath1069.60010OpenAlexW1991348779MaRDI QIDQ4662232

Matthias Reitzner, Rolf Schneider, Daniel Hug

Publication date: 30 March 2005

Published in: Advances in Applied Probability (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1239/aap/1093962228

zbMATH Keywords

intrinsic volumeasymptotic shapePoisson-Voronoi tessellationtypical cellPoisson hyperplane tessellationKendall's conjecture

Mathematics Subject Classification ID

Geometric probability and stochastic geometry (60D05) Inequalities and extremum problems involving convexity in convex geometry (52A40) Random convex sets and integral geometry (aspects of convex geometry) (52A22)

Related Items (15)

Cell Shape Analysis of Random Tessellations Based on Minkowski Tensors ⋮ Cluster size distributions of extreme values for the Poisson-Voronoi tessellation ⋮ Distance from the nucleus to a uniformly random point in the 0-cell and the typical cell of the Poisson-Voronoi tessellation ⋮ Introduction to Stochastic Geometry ⋮ Faces of Poisson-Voronoi mosaics ⋮ Extreme values for characteristic radii of a Poisson-Voronoi tessellation ⋮ Asymptotic statistics of then-sided planar Poisson–Voronoi cell: II. Heuristics ⋮ Faces with given directions in anisotropic Poisson hyperplane mosaics ⋮ Random line tessellations of the plane: Statistical properties of many-sided cells ⋮ Large faces in Poisson hyperplane mosaics ⋮ On the correlation between the volumes of the typical Poisson-Voronoi cell and the typical Stienen sphere ⋮ The perimeter of large planar Voronoi cells: a double-stranded random walk ⋮ Asymptotic statistics of then-sided planar Poisson–Voronoi cell: I. Exact results ⋮ Fractal random series generated by Poisson-Voronoi tessellations ⋮ Limit theorems for the typical Poisson-Voronoi cell and the Crofton cell with a large inradius

Cites Work

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• Stability of inequalities in the dual Brunn-Minkowski theory
• On a conjecture of D. G. Kendall concerning the planar Crofton cell and on its Brownian counterpart
• Lectures on random Voronoi tessellations
• A simplified proof of a conjecture of D. G. Kendall concerning shapes of random polygons
• The limit shape of the zero cell in a stationary Poisson hyperplane tessellation.
• Large cells in Poisson-Delaunay tessellations
• Stability Estimates for some Geometric Inequalities
• The distributions of the smallest disks containing the Poisson-Voronoi typical cell and the Crofton cell in the plane
• A heuristic proof of a long-standing conjecture of D. G. Kendall concerning the shapes of certain large random polygons

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