A Strong Correlation Inequality for Contact Processes and Oriented Percolation

Vladimir Belitsky, Pablo A. Ferrari, Norio Konno, Thomas M. Liggett

Let $\nu (A)$ be the extinction probability for a contact process on a countable set $S$ with initial state $A\subset S$. We prove that for any sets $A, B\subset S$, $$\nu (A\cap B)\nu (A\cup B)\geq \nu (A)\nu (B).$$ We also prove an analogous statement for oriented percolation.

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Last modified: Fri Dec 6 18:05:33 EDT 1996