Poisson polytopes

DOI10.1214/09-AOP514zbMath1204.60018arXiv1010.3582OpenAlexW3037501403MaRDI QIDQ989185

Matthias Reitzner, Imre Bárány

Publication date: 30 August 2010

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

Full work available at URL: https://arxiv.org/abs/1010.3582

zbMATH Keywords

central limit theoremapproximation of convex bodiesrandom polytopesdependency graph.

Mathematics Subject Classification ID

Geometric probability and stochastic geometry (60D05) Strong limit theorems (60F15) Combinatorial probability (60C05) Random convex sets and integral geometry (aspects of convex geometry) (52A22)

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Convex Hulls of Uniform Samples from a Convex Polygon ⋮ Variance asymptotics and scaling limits for random polytopes ⋮ From proximity to utility: a Voronoi partition of Pareto optima ⋮ CONVEX CURVES AND A POISSON IMITATION OF LATTICES ⋮ Asymptotic Methods for Random Tessellations ⋮ A central limit theorem for projections of the cube ⋮ Variance expansion and Berry-Esseen bound for the number of vertices of a random polygon in a polygon ⋮ The duality of the volumes and the numbers of vertices of random polytopes ⋮ Introduction to Stochastic Geometry ⋮ Limit theory for the first layers of the random convex hull peeling in the unit ball ⋮ Brownian limits, local limits and variance asymptotics for convex hulls in the ball ⋮ Concentration and moderate deviations for Poisson polytopes and polyhedra ⋮ Variance asymptotics for random polytopes in smooth convex bodies ⋮ Methods for estimation of convex sets ⋮ Central limit theorems for random polygons in an arbitrary convex set ⋮ Beyond the Efron-Buchta identities: distributional results for Poisson polytopes ⋮ The scaling limit of Poisson-driven order statistics with applications in geometric probability ⋮ Central limit theorems for uniform model random polygons ⋮ Intrinsic volumes of inscribed random polytopes in smooth convex bodies ⋮ Multivariate normal approximation for functionals of random polytopes ⋮ Interaction of Poisson hyperplane processes and convex bodies

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• [https://portal.mardi4nfdi.de/wiki/Publication:5728818 �ber die konvexe H�lle von n zuf�llig gew�hlten Punkten]

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