Limit theorems for functionals of convex hulls

DOI10.1007/BF01204952zbMath0808.60019OpenAlexW2465596012MaRDI QIDQ1336265

A. J. Cabo, Piet Groeneboom

Publication date: 15 March 1995

Published in: Probability Theory and Related Fields (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01204952

zbMATH Keywords

extreme pointscentral limit theoremconvex hullPoisson point processprobabilistic behavior

Mathematics Subject Classification ID

Geometric probability and stochastic geometry (60D05) Central limit and other weak theorems (60F05) Martingales with continuous parameter (60G44) Length, area, volume and convex sets (aspects of convex geometry) (52A38) Point processes (e.g., Poisson, Cox, Hawkes processes) (60G55) Random convex sets and integral geometry (aspects of convex geometry) (52A22)

Related Items (23)

On joint probability distribution of the number of vertices and area of the convex hulls generated by a Poisson point process ⋮ Convex Hulls of Uniform Samples from a Convex Polygon ⋮ A random approximation of set valued càdlàg functions ⋮ Central limit theorems for Gaussian polytopes ⋮ Unnamed Item ⋮ Introduction to Stochastic Geometry ⋮ Random points and lattice points in convex bodies ⋮ Concentration and moderate deviations for Poisson polytopes and polyhedra ⋮ On the variance of random polytopes ⋮ Properties of convex hull generated by inhomogeneous Poisson point process ⋮ Random polytopes and the Efron-Stein jackknife inequality. ⋮ Exact Formulae for Variances of Functionals of Convex Hulls ⋮ Variance asymptotics and central limit theorems for generalized growth processes with applications to convex hulls and maximal points ⋮ Central limit theorems for random polygons in an arbitrary convex set ⋮ Random convex hulls and extreme value statistics ⋮ A fast algorithm to sample the number of vertexes and the area of the random convex hull on the unit square ⋮ Geodesics and flows in a Poissonian city ⋮ Poisson polytopes ⋮ On resampling schemes for polytopes ⋮ Approximation of convex sets by polytopes ⋮ Asymptotic geometry of high-density smooth-grained Boolean models in bounded domains ⋮ Central limit theorems for random polytopes ⋮ On Limit Theorem for the Number of Vertices of the Convex Hulls in a Unit Disk

Cites Work

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• Limit theorems for convex hulls
• Stochastische Approximation konvexer Polygone
• The convex hull of a random set of points
• [https://portal.mardi4nfdi.de/wiki/Publication:5728818 �ber die konvexe H�lle von n zuf�llig gew�hlten Punkten]

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