an:01134829
Zbl 0890.60094
Belitsky, V.; Ferrari, P. A.; Konno, N.; Liggett, T. M.
A strong correlation inequality for contact processes and oriented percolation
EN
Stochastic Processes Appl. 67, No. 2, 213-225 (1997).
00047580
1997
j
60K35 82C22
contact process; oriented percolation; extinction probability; correlation inequality
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.
Petr Holick?? (Praha)