A strong correlation inequality for contact processes and oriented percolation
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.
scientific article; zbMATH DE number 1134829