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Random size trees on the one and two dimensional integer lattice

Published online by Cambridge University Press:  14 July 2016

A.M.V. Verhagen
A.M.V. Verhagen*
Affiliation:
Division of Mathematical Statistics, C.S.I.R.O., Melbourne
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Abstract

A stochastic process in which any tree in a forest planted on an integer lattice eliminates its four neighbours when it exceeds their heights, is studied for the case when all heights are independent samples from a continuous distribution. The proportion of the trees of the forest eliminated in this manner is determined for both the one and the two dimensional integer lattices.

Type
Research Papers
Information
Journal of Applied Probability , Volume 6 , Issue 2 , August 1969 , pp. 301 - 308
Copyright
Copyright © Sheffield: Applied Probability Trust 

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References

Baker, B. G. (1966) Configurational entropy of adsorption of large atoms. J. Chem. Phys. 45, 2694–2697.Google Scholar
Czarnowski, M. S. (1961) Dynamics of even aged forest stands. Louisiana State University Studies. Biological Sciences Series, Number 4.Google Scholar