Complete convergence theory of the contact process on \(T_d \times Z\) (Q812445)

The author consider the contact process on a branching plane \(T_d \times Z\) (\(T_d\) is a regular tree where every vertex has exactly \(d+1\) neighbors). It was shown by Pemantle in 1992 that the contact process on \(T_d\) has at least two different critical points. The author shows that the same is true for the contact process on \(T_d \times Z\) and proves complete convergence theorem above the second critical point.