Random spheres in a convex body
type: Item
instance of: scholarly article
title: Random spheres in a convex body
zbMATH Open document ID: 0671.60008
DOI: 10.1007/BF01199118
author: Fernando Affentranger
published in: Archiv der Mathematik
publication date: 1990-01-01T00:00:00Z
review text: In d-dimensional Euclidean space \(E^ d(d\geq 2)\) a convex body k is given and \(m+1\), \(2\leq m\leq d\), points \(X_ 0,...,X_ m\) are chosen independently and uniformly at random in K. The probability p(K; m-1) that the (m-1)-dimensional circumsphere \(C_{m-1}\) of \(X_ 0,...,X_ m\) is entirely contained in K is determined for \(m=d\) and some extremal properties are given. For instance, p(K; d-1) is maximal if and only if K is a ball. For the case where K is the d-dimensional unit ball, the investigations are extended to m, \(2\leq m\leq d\).
Mathematics Subject Classification ID: 60D05
Mathematics Subject Classification ID: 52A22
zbMATH DE Number: 4098380
zbMATH Keywords: geometric probabilities
zbMATH Keywords: uniform random points in a convex body
zbMATH Keywords: extremal properties
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4098380