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A correlation inequality for connection events in percolation. (English) Zbl 1013.60079

Summary: It is well-known in percolation theory (and intuitively plausible) that two events of the form “there is an open path from \(s\) to \(a\)” are positively correlated. We prove the (not intuitively obvious) fact that this is still true if we condition on an event of the form “there is no open path from \(s\) to \(t\)”.

MSC:

60K35 Interacting random processes; statistical mechanics type models; percolation theory
60C05 Combinatorial probability
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