On the correlation between the volumes of the typical Poisson-Voronoi cell and the typical Stienen sphere
Journal article, 2007

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.

Stienen model

Robbins' formula

Voronoi tessellation

typical cell

Poisson process

Correlation

Author

Viktor Olsbo

Chalmers, Mathematical Sciences, Mathematical Statistics

University of Gothenburg

Advances in Applied Probability

0001-8678 (ISSN) 1475-6064 (eISSN)

Vol. 39 4 883-892

Subject Categories

Other Mathematics

More information

Created

10/6/2017