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Radial generation of n-dimensional poisson processes

Published online by Cambridge University Press:  14 July 2016

M. P. Quine  and
D. F. Watson
M. P. Quine
Affiliation:
University of Sydney
D. F. Watson*
Affiliation:
University of Sydney
*
∗Postal address: Department of Mathematical Statistics, The University of Sydney, NSW 2006, Australia.
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Abstract

A simple method is proposed for the generation of successive ‘nearest neighbours' to a given origin in an n-dimensional Poisson process. It is shown that the method provides efficient simulation of random Voronoi polytopes. Results are given of simulation studies in two and three dimensions.

Keywords

GEOMETRICAL PROBABILITYSIMULATIONVORONOI POLYTOPE
Type
Research Papers
Information
Journal of Applied Probability , Volume 21 , Issue 3 , September 1984 , pp. 548 - 557
Copyright
Copyright © Applied Probability Trust 1984 

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References

[1] Crain, I. K. (1972) Monte-Carlo simulation of the random Voronoi polygons: preliminary results. Search 3, 220–221.Google Scholar
[2] Crain, I. K. and Miles, R. E. (1976) Monte-Carlo estimates of the distributions of the random polygons determined by random lines in a plane. J. Statist. Comput. Simul. 4, 293–325.CrossRefGoogle Scholar
[3] Deltheil, R. (1926) Probabilités géométriques. Traité du calcul des probabilités et de ses applications. Gauthier-Villars, Paris.Google Scholar
[4] Finney, J. L. (1970) Random packings and the structure of simple liquids I. The geometry of random close packing. Proc. R. Soc. London A 319, 479–493.Google Scholar
[5] Finney, J. L. (1970) Random packings and the structure of simple liquids II. The molecular geometry of simple liquids. Proc. R. Soc. London A 319, 495–507.Google Scholar
[6] Gilbert, E. N. (1962) Random subdivisions of space into crystals. Ann. Math. Statist. 33, 958–972.CrossRefGoogle Scholar
[7] Hammersley, J. M. (1972) Stochastic models for the distribution of particles in space. Suppl. Adv. Appl. Prob., 47–65.CrossRefGoogle Scholar
[8] Hinde, A. L. and Miles, R. E. (1980) Monte-Carlo estimates of the distributions of the random polygons of the Voronoi tessellation with respect to a Poisson process. J. Statist. Comput. Simul. 10, 205–223.CrossRefGoogle Scholar
[9] Kendall, M. G. (1961) A Course in the Geometry of n Dimensions. Griffin, London.Google Scholar
[10] Kendall, M. G. and Moran, P. A. P. (1963) Geometrical Probability. Griffin, London.Google Scholar
[11] Matheron, G. (1975) Random Sets and Integral Geometry. Wiley, New York.Google Scholar
[12] Meijering, J. L. (1953) Interface area, edge length and number of vertices in crystal aggregates with random nucleation. Philips Res. Rep. 8, 270–290.Google Scholar
[13] Miles, R. E. (1961) Random Polytopes: The Generalisation to n Dimensions of the Intervals of a Poisson Process. , University of Cambridge.Google Scholar
[14] Miles, R. E. and Maillardet, R. J. (1982) The basic structures of Voronoi and generalized Voronoi polygons. J. Appl. Prob. 19A, 97–111.CrossRefGoogle Scholar
[15] Renyi, A. (1967) Remarks on the Poisson process. In Lecture Notes in Mathematics 31, Springer-Verlag, Berlin, 280–286.Google Scholar
[16] Watson, D. F. (1981) Computing the n-dimensional Delaunay tessellation with application to Voronoi polytopes. Computer J. 24, 167–172.CrossRefGoogle Scholar
[17] Wendel, J. G. (1962) A problem in geometric probability. Math. Scand. 11, 109–111.CrossRefGoogle Scholar