Convex Hulls of Uniform Samples from a Convex Polygon

DOI10.1239/aap/1339878714zbMath1251.60011arXiv1109.3118OpenAlexW2963873837MaRDI QIDQ2898908

Piet Groeneboom

Publication date: 12 July 2012

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

Full work available at URL: https://arxiv.org/abs/1109.3118

zbMATH Keywords

convex polygonconvex hullPoisson point process

Mathematics Subject Classification ID

Geometric probability and stochastic geometry (60D05) Central limit and other weak theorems (60F05) Point processes (e.g., Poisson, Cox, Hawkes processes) (60G55) Random convex sets and integral geometry (aspects of convex geometry) (52A22)

Related Items (8)

On joint probability distribution of the number of vertices and area of the convex hulls generated by a Poisson point process ⋮ Unnamed Item ⋮ The duality of the volumes and the numbers of vertices of random polytopes ⋮ ON RANDOM CONVEX CHAINS, ORTHOGONAL POLYNOMIALS, PF SEQUENCES AND PROBABILISTIC LIMIT THEOREMS ⋮ Properties of convex hull generated by inhomogeneous Poisson point process ⋮ Exact Formulae for Variances of Functionals of Convex Hulls ⋮ Zeros of random tropical polynomials, random polygons and stick-breaking ⋮ On Limit Theorem for the Number of Vertices of the Convex Hulls in a Unit Disk

Cites Work

• Unnamed Item
• Vertices of the least concave majorant of Brownian motion with parabolic drift
• Poisson polytopes
• The concave majorant of Brownian motion
• Limit theorems for convex hulls
• Limit theorems for functionals of convex hulls
• An identity relating moments of functionals of convex hulls
• Some properties of convex hulls generated by homogeneous Poisson point processes in an unbounded convex domain
• On the variance of random polytopes
• On the boundary structure of the convex hull of random points

This page was built for publication: Convex Hulls of Uniform Samples from a Convex Polygon