Subcritical branching processes in a two-state random environment, and a percolation problem on trees

Abstract

We determine the decay rate of the survival probability of subcritical branching processes in a two-state random environment, where one state is subcritical, the other supercritical. This result is applied to obtain the asymptotic behavior (asn→∞) of the number of different words of lengthnoccurring on the binary, and generally theb-ary, tree with Bernoulli percolation.