The law of the smallest disk containing the typical Poisson-Voronoi cell
type: Item
instance of: scholarly article
title: The law of the smallest disk containing the typical Poisson-Voronoi cell
zbMATH Open document ID: 0999.60008
DOI: 10.1016/S1631-073X(02)02261-6
author: Pierre Calka
published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris
publication date: 2002-08-04T00:00:00Z
review text: Let \(R_m\) \((R_M)\) denote the radius of the largest (smallest) disk centered at the origin which is included in (respectively, contains) the typical cell of the two-dimensional Poisson-Voronoi tessellation. Based on covering properties of the circle due to \textit{A. F. Siegel} [J. Appl. Probab. 15, 340-355 (1978; Zbl 0391.60017)] and \textit{A. F. Siegel} and \textit{L. Holst} [ibid. 19, 373-381 (1982; Zbl 0489.60017)] the author obtains the joint distribution of \(R_m\) and \(R_M\).
reviewed by: Klaus Schürger
Mathematics Subject Classification ID: 60D05
zbMATH DE Number: 1744354
zbMATH Keywords: two-dimensional Poisson-Voronoi tessellation
zbMATH Keywords: covering properties
MaRDI profile type: Publication
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full work available at URL: s1631-073x(02)02261-6
OpenAlex ID: W2049965164
description: scientific article; zbMATH DE number 1744354