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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

Citations:

Zbl 0616.60097
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