# zbMATH — the first resource for mathematics

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