Random polytopes in a convex polytope, independence of shape, and concentration of vertices

DOI10.1007/BF01459511zbMath0788.52003OpenAlexW2035918852MaRDI QIDQ1318141

Imre Bárány, Christian Buchta

Publication date: 12 April 1994

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/165141

zbMATH Keywords

convex polytopeconvex hullrandom points

Mathematics Subject Classification ID

Geometric probability and stochastic geometry (60D05) Random convex sets and integral geometry (aspects of convex geometry) (52A22)

Related Items (24)

On statistical learning of simplices: unmixing problem revisited ⋮ Best and random approximation of a convex body by a polytope ⋮ Variance asymptotics and scaling limits for random polytopes ⋮ Unnamed Item ⋮ New perspectives and computational challenges in high dimensions. Abstracts from the workshop held February 2--8, 2020 ⋮ Variance expansion and Berry-Esseen bound for the number of vertices of a random polygon in a polygon ⋮ Uniform behaviors of random polytopes under the Hausdorff metric ⋮ Introduction to Stochastic Geometry ⋮ The convex hull of random points on the boundary of a simple polytope ⋮ Random points and lattice points in convex bodies ⋮ Deviation inequalities for random polytopes in arbitrary convex bodies ⋮ On the variance of random polytopes ⋮ Random polytopes and the Efron-Stein jackknife inequality. ⋮ Methods for estimation of convex sets ⋮ Exact Formulae for Variances of Functionals of Convex Hulls ⋮ The combinatorial structure of random polytopes ⋮ Random points on the boundary of smooth convex bodies ⋮ Poisson polytopes ⋮ Flag numbers and floating bodies ⋮ Approximation of convex sets by polytopes ⋮ Mean width of random polytopes in a reasonably smooth convex body ⋮ Expectation of intrinsic volumes of random polytopes ⋮ Sylvester's problem for symmetric convex bodies and related problems ⋮ Central limit theorems for random polytopes

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Intrinsic volumes and f-vectors of random polytopes
• Über die konvexe Hülle von Zufallspunkten in Eibereichen
• A note on the volume of a random polytope in a tetrahedron
• A note on finding convex hulls via maximal vectors
• The convex floating body and polyhedral approximation
• Unsolved problems in geometry
• Random points in a simplex
• On the mean value of the volume of a random polytope in a convex set
• On the convex hull of uniform random points in a simple \(d\)-polytope
• A theorem on non-homogeneous lattices
• The Historical Development of J. J. Sylvester's Four Point Problem
• Zufallspolygone in konvexen Vielecken.
• On the convex hull of random points in a polytope
• Convex bodies, economic cap coverings, random polytopes
• On the mean value of the area of a random polygon in a plane convex body
• On the Average Number of Maxima in a Set of Vectors and Applications
• The convex hull of a uniform sample from the interior of a simple d-polytope
• Random approximation of convex sets*
• The convex hull of a random set of points
• The directions of the line segments and of the r ‐dimensional balls on the boundary of a convex body in Euclidean space
• [https://portal.mardi4nfdi.de/wiki/Publication:5728818 �ber die konvexe H�lle von n zuf�llig gew�hlten Punkten]

This page was built for publication: Random polytopes in a convex polytope, independence of shape, and concentration of vertices