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A new proof of the complete convergence theorem for contact processes in several dimensions with large infection parameter. (English) Zbl 0616.60097

The author proves the convergence theorem for the multidimensional contact process with large coupling (”infection”) parameter using the reduction to special imbedded one-dimensional contact processes. More exactly, let \(\lambda_ 1\) be the critical value of the coupling constant in the one-dimensional contact process, then the multidimensional contact process has a unique (steady) state for any \(\lambda >\lambda_ 1\). The proof is rather elementary but uses the notion of contact processes with percolation structures.
Reviewer: V.Chulaevsky

MSC:

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