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Intermediate phase for the contact process on a tree. (English) Zbl 0830.60093
The authors consider the contact process on a homogeneous tree in which \(k \geq 3\) branches emanate for each vertex of the tree. They study the extremal nontranslation invariant stationary distributions with birth rate taking values between the two critical values (corresponding to global survival and local survival of the contact process). They prove that for such a rate, there are infinitely many extremal stationary distributions. A main step is to use a correspondence between a stationary measure for the contact process and a harmonic function for the dual.

MSC:
60K35 Interacting random processes; statistical mechanics type models; percolation theory
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