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The random division of faces in a planar graph

Published online by Cambridge University Press:  01 July 2016

Richard Cowan*
Affiliation:
University of Hong Kong
Simone Chen*
Affiliation:
University of Hong Kong
*
Postal address: Department of Statistics, The University of Hong Kong, Pokfulam Road, Hong Kong.
Postal address: Department of Statistics, The University of Hong Kong, Pokfulam Road, Hong Kong.

Abstract

A planar graph contains faces which can be classified into types depending on the number of edges on the face boundaries. Under various natural rules for randomly dividing faces by the addition of new edges, we investigate the limiting distribution of face type as the number of divisions increases.

Type
Stochastic Geometry and Statistical Applications
Copyright
Copyright © Applied Probability Trust 1996 

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References

Cowan, R. (1989) The division of space and the Poisson distribution. Adv. Appl. Prob. 21, 233234.CrossRefGoogle Scholar
Cowan, R. and Chen, S. (1996) The random topology of polygon splitting. In preparation.Google Scholar
Cowan, R. and Morris, V. B. (1988) Division rules for polygonal cells. J. Theor. Biol. 131, 3342.Google Scholar
Cox, D. R. and Miller, H. D. (1965) The Theory of Stochastic Processes. Methuen, London.Google Scholar