A new proof of the complete convergence theorem for contact processes in several dimensions with large infection parameter (Q1821432)
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scientific article; zbMATH DE number 3998944
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A new proof of the complete convergence theorem for contact processes in several dimensions with large infection parameter |
scientific article; zbMATH DE number 3998944 |
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A new proof of the complete convergence theorem for contact processes in several dimensions with large infection parameter (English)
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1987
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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.
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contact process
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critical value of the coupling constant
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contact processes with percolation structures
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