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The proportion of triangles in a Poisson-Voronoi tessellation of the plane

Part of: Geometric probability and stochastic geometry Stochastic processes

Published online by Cambridge University Press:  01 July 2016

Andrew Hayen  and
Malcolm Quine
Andrew Hayen*
Affiliation:
University of Sydney
Malcolm Quine*
Affiliation:
University of Sydney
*
∗ Postal address: School of Mathematics and Statistics, University of Sydney, NSW 2006, Australia.
∗ Postal address: School of Mathematics and Statistics, University of Sydney, NSW 2006, Australia.
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Abstract

By using an adaptation of the radial generation method, we give an integral formula for the proportion of triangles in a Poisson-Voronoi tessellation, which gives a value of 0.0112354 to 7 decimal places. We also obtain the first four moments of some characteristics of triangles.

Keywords

PoissonVoronoitessellationPalm probabilitytrianglemoments

MSC classification

Primary: 60D05: Geometric probability and stochastic geometry
Secondary: 60G55: Point processes
Type
Stochastic Geometry and Statistical Applications
Information
Advances in Applied Probability , Volume 32 , Issue 1 , March 2000 , pp. 67 - 74
Copyright
Copyright © Applied Probability Trust 2000 

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