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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

Cut-set sums and tree processes


Author: K. J. Falconer
Journal: Proc. Amer. Math. Soc. 101 (1987), 337-346
MSC: Primary 90B10; Secondary 60G48, 60J80, 90B15
MathSciNet review: 902553
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Abstract: Suppose that an infinite tree has a value assigned to each vertex. We obtain estimates for the sums of such values over cut-sets of the tree. For certain tree processes, where the values are given by random variables, we investigate the almost sure behavior of such cut-set sums. Processes of this type arise in problems concerning random fractals and flows in random networks.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1987-0902553-7
PII: S 0002-9939(1987)0902553-7
Keywords: Tree process, network flow, branching process, random fractal
Article copyright: © Copyright 1987 American Mathematical Society