Central limit theorems for uniform model random polygons

DOI10.1007/s10959-010-0335-2zbMath1258.60026arXiv1110.5656OpenAlexW3106264566MaRDI QIDQ715751

John Pardon

Publication date: 1 November 2012

Published in: Journal of Theoretical Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1110.5656

zbMATH Keywords

central limit theoremrandom polygons

Mathematics Subject Classification ID

Geometric probability and stochastic geometry (60D05) Central limit and other weak theorems (60F05) Convex sets in (2) dimensions (including convex curves) (52A10) Random convex sets and integral geometry (aspects of convex geometry) (52A22)

Related Items (12)

On joint probability distribution of the number of vertices and area of the convex hulls generated by a Poisson point process ⋮ Variance bounds for disc-polygons ⋮ Unnamed Item ⋮ Variance expansion and Berry-Esseen bound for the number of vertices of a random polygon in a polygon ⋮ Introduction to Stochastic Geometry ⋮ Deviation inequalities for random polytopes in arbitrary convex bodies ⋮ Properties of convex hull generated by inhomogeneous Poisson point process ⋮ Methods for estimation of convex sets ⋮ Exact Formulae for Variances of Functionals of Convex Hulls ⋮ Random polytopes: Central limit theorems for intrinsic volumes ⋮ Central limit theorems for random polygons in an arbitrary convex set ⋮ Interaction of Poisson hyperplane processes and convex bodies

Cites Work

• Central limit theorems for random polygons in an arbitrary convex set
• Central limit theorems for random polytopes in a smooth convex set
• Poisson polytopes
• On the variance of random polytopes
• Central limit theorems for random polytopes
• Upper bounds for the distance in total variation between the binomial or negative binomial and the Poisson distribution

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