Large planar Poisson-Voronoi cells containing a given convex body

DOI10.5802/ahl.86zbMath1483.52002OpenAlexW3196135527MaRDI QIDQ2077172

Pierre Calka, Yann Demichel, Nathanaël Enriquez

Publication date: 24 February 2022

Published in: Annales Henri Lebesgue (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.5802/ahl.86

zbMATH Keywords

support functionSteiner pointPoisson-Voronoi tessellationVoronoi flowerEfron identity

Mathematics Subject Classification ID

Geometric probability and stochastic geometry (60D05) Point processes (e.g., Poisson, Cox, Hawkes processes) (60G55) Random convex sets and integral geometry (aspects of convex geometry) (52A22) Asymptotic theory of convex bodies (52A23)

Related Items (2)

Mini-workshop: A geometric fairytale full of spectral gaps and random fruit. Abstracts from the mini-workshop held November 27 -- December 3, 2022 ⋮ Elongated Poisson-Voronoi cells in an empty half-plane

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Variance asymptotics and scaling limits for random polytopes
• A law of the single logarithm for weighted sums of i.i.d. random elements
• Lectures on random Voronoi tessellations
• Contributions to affine surface area
• Approximation of smooth convex bodies by random circumscribed polytopes
• The limit shape of the zero cell in a stationary Poisson hyperplane tessellation.
• The Brunn-Minkowski-Firey theory. II: Affine and geominimal surface areas
• Brownian limits, local limits and variance asymptotics for convex hulls in the ball
• Poisson polyhedra in high dimensions
• Variance asymptotics for random polytopes in smooth convex bodies
• Limit theorems for the typical Poisson-Voronoi cell and the Crofton cell with a large inradius
• Approximation Properties of Random Polytopes Associated with Poisson Hyperplane Processes
• Weighted faces of Poisson hyperplane tessellations
• Estimates for distributions of the Voronoi polygon's geometric characteristics
• On a Voronoi aggregative process related to a bivariate Poisson process
• Asymptotic estimates for best and stepwise approximation of convex bodies III
• POISSON HYPERPLANE PROCESSES AND APPROXIMATION OF CONVEX BODIES
• [https://portal.mardi4nfdi.de/wiki/Publication:5331598 �ber die konvexe H�lle von n zuf�llig gew�hlten Punkten. II]
• The convex hull of a random set of points
• ZufÄllige konvexe Polygone in einem Ringgebiet
• [https://portal.mardi4nfdi.de/wiki/Publication:5728818 �ber die konvexe H�lle von n zuf�llig gew�hlten Punkten]

This page was built for publication: Large planar Poisson-Voronoi cells containing a given convex body