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A mosaic of triangular cells formed with sequential splitting rules

Part of: Markov processes Theory of computing Distribution theory - Probability Geometric probability and stochastic geometry Discrete mathematics in relation to computer science

Published online by Cambridge University Press:  14 July 2016

Richard Cowan
Richard Cowan*
Affiliation:
School of Mathematics and Statistics, University of Sydney, NSW 2006, Australia. Email address: richardc@maths.usyd.edu.au
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Abstract

The iterative division of a triangle by chords which join a randomly-selected vertex of a triangle to the opposite side is investigated. Results on the limiting random graph which eventuates are given. Aspects studied are: the order of vertices; the fragmentation of chords; age distributions for elements of the graph; various topological characterisations of the triangles. Different sampling protocols are explored. Extensive use is made of the theory of branching processes.

Keywords

Random topologyrandom geometrydistribution theorybranching processesdivision of space

MSC classification

Primary: 60D05: Geometric probability and stochastic geometry 60E05: Distributions 60J80: Branching processes (Galton-Watson, birth-and-death, etc.) 68Q80: Cellular automata 68R10: Graph theory (including graph drawing)
Type
Part 1. Branching processes
Information
Journal of Applied Probability , Volume 41 , Issue A: Stochastic Methods and their Applications , 2004 , pp. 3 - 15
Copyright
Copyright © Applied Probability Trust 2004 

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References

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