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Van den Berg-Kesten inequality for the Poisson Boolean model for continuum percolation. (English) Zbl 0977.60100
Summary: For the Poisson Boolean model of continuum percolation we prove the Van den Berg-Kesten inequality \(P(A\square B)\leq P(A)P(B)\) for any two events \(A\) and \(B\) living on a bounded region.

MSC:
60K35 Interacting random processes; statistical mechanics type models; percolation theory
82B43 Percolation
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