The limit shape of the zero cell in a stationary Poisson hyperplane tessellation.

DOI10.1214/aop/1079021474zbMath1050.60010OpenAlexW1998334355MaRDI QIDQ1879879

Rolf Schneider, Daniel Hug, Matthias Reitzner

Publication date: 15 September 2004

Published in: The Annals of Probability (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1214/aop/1079021474

zbMATH Keywords

asymptotic shapeCrofton celltypical cellzero cellKendall's conjecturePoisson hyperplane processhyperplane tessellation

Mathematics Subject Classification ID

Geometric probability and stochastic geometry (60D05) Random convex sets and integral geometry (aspects of convex geometry) (52A22)

Related Items (21)

Weak convergence of the intersection point process of Poisson hyperplanes ⋮ On the Volume of the Zero Cell of a Class of Isotropic Poisson Hyperplane Tessellations ⋮ Stochastic Geometry to Generalize the Mondrian Process ⋮ Asymptotic Methods for Random Tessellations ⋮ Cells with many facets in a Poisson hyperplane tessellation ⋮ Doubly random polytopes ⋮ Introduction to Stochastic Geometry ⋮ Extremal behavior of large cells in the Poisson hyperplane mosaic ⋮ Short-length routes in low-cost networks via Poisson line patterns ⋮ Refined convergence for the Boolean model ⋮ Faces with given directions in anisotropic Poisson hyperplane mosaics ⋮ Stability of the reverse Blaschke-Santaló inequality for zonoids and applications ⋮ Asymptotic shape of small cells ⋮ Large Poisson-Voronoi cells and Crofton cells ⋮ Large faces in Poisson hyperplane mosaics ⋮ The stochastic geometry of unconstrained one-bit data compression ⋮ Three-dimensional random Voronoi tessellations: from cubic crystal lattices to Poisson point processes ⋮ Bayesian nonparametric binary regression via random tessellations ⋮ Large planar Poisson-Voronoi cells containing a given convex body ⋮ Limit theorems for the typical Poisson-Voronoi cell and the Crofton cell with a large inradius ⋮ Elongated Poisson-Voronoi cells in an empty half-plane

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• On an inequality of Minkowski for mixed volumes
• The approximation of convex sets by polyhedra
• Proof of David Kendall's conjecture concerning the shape of large random polygons
• On a conjecture of D. G. Kendall concerning the planar Crofton cell and on its Brownian counterpart
• A simplified proof of a conjecture of D. G. Kendall concerning shapes of random polygons
• Random hyperplanes meeting a convex body
• A heuristic proof of a long-standing conjecture of D. G. Kendall concerning the shapes of certain large random polygons

This page was built for publication: The limit shape of the zero cell in a stationary Poisson hyperplane tessellation.