## A proof of the complete convergence theorem for contact processes on some product graphs.(Chinese. English summary)Zbl 1224.60246

Summary: A proof of the complete convergence theorem for the basic contact process on the product graph $$G_1\times G_2\times \mathbb Z$$ is given, provided that the infection parameter is large enough, where $$G_1$$ and $$G_2$$ are arbitrary infinite locally finite transitive graphs. This extends, to some extent, the result of R. H. Schonmann [Ann. Probab. 15, 382–387 (1987; Zbl 0616.60097)].

### MSC:

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

### Keywords:

contact process; complete convergence theorem

Zbl 0616.60097