Poisson-Voronoi approximation

DOI10.1214/08-AAP561zbMath1172.60003arXiv0906.4238OpenAlexW2014156379MaRDI QIDQ1024903

Matthias Reitzner, Matthias Heveling

Publication date: 17 June 2009

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

Full work available at URL: https://arxiv.org/abs/0906.4238

zbMATH Keywords

valuationsPoisson point processapproximation of convex setsjackknife estimate of variancePoisson--Voronoi tessellation

Mathematics Subject Classification ID

Geometric probability and stochastic geometry (60D05) Combinatorial probability (60C05) Point processes (e.g., Poisson, Cox, Hawkes processes) (60G55) Random convex sets and integral geometry (aspects of convex geometry) (52A22)

Related Items

Phase transitions and noise sensitivity on the Poisson space via stopping sets and decision trees, Introduction to Stochastic Geometry, Boundary density and Voronoi set estimation for irregular sets, Extreme values for characteristic radii of a Poisson-Voronoi tessellation, Set Reconstruction by Voronoi Cells, A central limit theorem for the Poisson-Voronoi approximation, Surface order scaling in stochastic geometry, Poisson process Fock space representation, chaos expansion and covariance inequalities, Asymptotic theory for statistics of the Poisson-Voronoi approximation

Cites Work

• The jackknife estimate of variance
• Lectures on random Voronoi tessellations
• Foundations of quantization for probability distributions
• Laws of large numbers in stochastic geometry with statistical applications
• On the almost sure coverage property of Voronoi tessellation: the ℝ¹ case
• A short proof of Hadwiger's characterization theorem
• The two-sample problem in $\Bbb R\sp m$ and measure-valued martingales
• The bootstrap and Edgeworth expansion
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