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A strong correlation inequality for contact processes and oriented percolation. (English) Zbl 0890.60094
The strengthening of the positive correlation inequality $$\nu (A\cap B)\nu (A\cup B) \geq \nu (A)\nu (B)$$ is proved for the following two cases. The extinction probability $$\nu (A)$$ for the contact process on a countable set $$S$$ with initial state $$A\subset S$$, or equivalently, for $$\nu (A)=\nu _\infty (\{\eta ;\eta _A\equiv 0\})$$ with $$\nu _\infty$$ being the upper invariant measure of the contact process. The same inequality is independently proved for $$\nu$$ being the extinction probability of an oriented percolation which can be viewed as a discrete time version of the one-dimensional contact process.

##### MSC:
 60K35 Interacting random processes; statistical mechanics type models; percolation theory 82C22 Interacting particle systems in time-dependent statistical mechanics
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##### References:
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