Proof of David Kendall's conjecture concerning the shape of large random polygons
type: Item
instance of: scholarly article
title: Proof of David Kendall's conjecture concerning the shape of large random polygons
zbMATH Open document ID: 0922.60022
DOI: 10.1007/BF02733102
author: I. M. Kovalenko
published in: Cybernetics and Systems Analysis
publication date: 1999-04-28T00:00:00Z
review text: Let \(m(\omega)\) be a Poisson line process in the plane \(R^2\). The paper considers the tessellation of \(R^2\) into random polygons generated by \(m(\omega)\). ``Crofton cell'' \(K\) is the polygon which contains fixed point \(O\). \(A(K)\) is the area of \(K\). The main result: The shape \(\sigma(K)\) of a typical random polygon \(K\) of a large area is close to that of a disc (\(A(K)\to + \infty\)). For the entire collection see \textit{R. E. Miles} [Adv. Appl. Probab. 27, No. 2, 397-417 (1995; Zbl 0829.60008)].
Mathematics Subject Classification ID: 60D05
Mathematics Subject Classification ID: 52A22
zbMATH DE Number: 1262968
zbMATH Keywords: random polygon
zbMATH Keywords: Poisson line process
zbMATH Keywords: tessellation
Wikidata QID: Q123360376
reviewed by: Viktor Ohanyan
MaRDI profile type: Publication
cites work: Q3759605
cites work: A heuristic proof of a long-standing conjecture of D. G. Kendall concerning the shapes of certain large random polygons
cites work: Shape Manifolds, Procrustean Metrics, and Complex Projective Spaces
cites work: RANDOM POLYGONS DETERMINED BY RANDOM LINES IN A PLANE
cites work: The various aggregates of random polygons determined by random lines in a plane
cites work: Q3866823
full work available at URL: https://doi.org/10.1007/bf02733102
OpenAlex ID: W2002003673
description: scientific article; zbMATH DE number 1262968