Subcritical Branching Processes in a Two State Random Environment, and a Percolation Problem on Trees

摘要

The decay rate of the survival probability of subcritical branching processes in a two state random environment is determined, where one state is subcritical, the other supercritical. The result is applied to obtain the asymptotic behavior (as n tends to infinity) of the number of different words of length n occurring on the binary, and generally the b-ary, tree with Bernoulli percolation. (Copyright (c) 1986 by Department of Mathematics and Informatics, Delft, The Netherlands.)