On the convex hull of uniform random points in a simple \(d\)-polytope

DOI10.1007/BF02574691zbMath0725.52004MaRDI QIDQ2276760

Fernando Affentranger, John André Wieacker

Publication date: 1991

Published in: Discrete \& Computational Geometry (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/131160

zbMATH Keywords

random polytopessimple polytopesexpected volumemean volumeexpected number of verticesconvex hull of n random pointsexpected number of facets

Mathematics Subject Classification ID

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

Related Items (16)

Expected size of random Tukey layers and convex layers ⋮ Best and random approximation of a convex body by a polytope ⋮ PROBABILISTIC ANALYSIS FOR DISCRETE ATTRIBUTES OF MOVING POINTS ⋮ Uniform behaviors of random polytopes under the Hausdorff metric ⋮ 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 ⋮ The smoothed complexity of Frank-Wolfe methods via conditioning of random matrices and polytopes ⋮ Distribution-independent properties of the convex hull of random points ⋮ On the variance of random polytopes ⋮ The combinatorial structure of random polytopes ⋮ Uniform generation in spatial constraint databases and applications ⋮ Approximation of convex sets by polytopes ⋮ Random convex hulls in a product of balls ⋮ Expectation of intrinsic volumes of random polytopes ⋮ Random polytopes in a convex polytope, independence of shape, and concentration of vertices

Cites Work

• Intrinsic volumes and f-vectors of random polytopes
• A note on the volume of a random polytope in a tetrahedron
• Random points in a simplex
• On some mean values associated with a randomly selected simplex in a convex set
• Stochastische Approximation konvexer Polygone
• On the convex hull of random points in a polytope
• Convex bodies, economic cap coverings, random polytopes
• The convex hull of a uniform sample from the interior of a simple d-polytope
• Random approximation of convex sets*
• [https://portal.mardi4nfdi.de/wiki/Publication:5331598 �ber die konvexe H�lle von n zuf�llig gew�hlten Punkten. II]
• 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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