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On the correlation between the volumes of the typical Poisson-Voronoi cell and the typical Stienen sphere

Viktor Olsbo (Institutionen för matematiska vetenskaper, matematisk statistik)
Advances in Applied Probability (0001-8678). Vol. 39 (2007), 4, p. 883-892.
[Artikel, refereegranskad vetenskaplig]

In this paper we consider a tessellation V generated by a homogeneous Poisson process Φ in Rd and, furthermore, the random set of spheres with centres being the points in Φ and having radii equal to half the distance to their closest neighbouring point in Φ. In Rd we give an integral formula for the correlation between the volume of the typical cell and the volume of the sphere in the typical cell, and we also show that this correlation is strictly positive. Furthermore, on the real line we give an analytical expression for the correlation, and in the plane and in space we give simplified integral formulae. Numerical values for the correlation for d = 2,...,7 are also given.

Nyckelord: Correlation; Poisson process; Robbins' formula; Stienen model; typical cell; Voronoi tessellation



Denna post skapades 2008-01-10.
CPL Pubid: 65558

 

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Institutioner (Chalmers)

Institutionen för matematiska vetenskaper, matematisk statistik (2005-2016)

Ämnesområden

Annan matematik

Chalmers infrastruktur