Sylvester's question: The probability that \(n\) points are in convex position

DOI10.1214/aop/1022677559zbMath0959.60006OpenAlexW2389044384MaRDI QIDQ1577749

Imre Bárány

Publication date: 26 April 2001

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

Full work available at URL: https://doi.org/10.1214/aop/1022677559

zbMATH Keywords

limit shapeaffine perimeterrandom points in convex position

Mathematics Subject Classification ID

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

Related Items (17)

Expected size of random Tukey layers and convex layers ⋮ Asymptotics of convex lattice polygonal lines with a constrained number of vertices ⋮ U-Statistics in Stochastic Geometry ⋮ Large convex holes in random point sets ⋮ Random points and lattice points in convex bodies ⋮ Central limit theorems for \(U\)-statistics of Poisson point processes ⋮ Affine surface area and convex bodies of elliptic type ⋮ Asymptotic statistics of then-sided planar Poisson–Voronoi cell: II. Heuristics ⋮ Lower bounds for the number of hyperplanes separating two finite sets of points ⋮ Extremal general affine surface areas ⋮ On maximal convex lattice polygons inscribed in a plane convex set ⋮ Nonnegative rank factorization -- a heuristic approach via rank reduction ⋮ \(\mathrm{SL}(n)\) invariant valuations on polytopes ⋮ General affine surface areas ⋮ Approximation of convex sets by polytopes ⋮ Sylvester’s question and the random acceleration process ⋮ Central limit theorems for random polytopes

This page was built for publication: Sylvester's question: The probability that \(n\) points are in convex position