When does the union of random spherical caps become connected?
type: Item
instance of: scholarly article
title: When does the union of random spherical caps become connected?
zbMATH Open document ID: 1064.60019
DOI: 10.1007/BF02530553
author: Xianqiang Yang
published in: Annals of the Institute of Statistical Mathematics
publication date: 2005-03-14T00:00:00Z
review text: Let \(U\) denote the part of the surface covered by \(N\) random spherical caps \(c_1, c_2,\dots,c_N\) of the same angular radius \(\Theta\) placed on the surface of a unit sphere in 3-space. It is proved that if \(c>\sqrt 2\), then the probability that \(U\) is connected tends to 1 as \(N\to 0\), while if \(c<1\), then the probability that \(U\) is connected tends to 0 as \(N\to\infty\).
Mathematics Subject Classification ID: 60D05
Mathematics Subject Classification ID: 60C05
zbMATH DE Number: 2145361
zbMATH Keywords: coverage problem
zbMATH Keywords: random spherical caps
reviewed by: N. G. Gamkrelidze
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02530553
OpenAlex ID: W2087657273
description: scientific article; zbMATH DE number 2145361