Cut-set sums and tree processes

Falconer, K. J.

doi:10.1090/S0002-9939-1987-0902553-7

Cut-set sums and tree processes
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Proc. Amer. Math. Soc. 101 (1987), 337-346 Request permission

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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