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Subcritical regimes in the Poisson Boolean model of continuum percolation. (English) Zbl 1148.60077
Summary: We consider the Poisson Boolean model of continuum percolation. We show that there is a subcritical phase if and only if $$E(R^d)$$ is finite, where $$R$$ denotes the radius of the balls around Poisson points and $$d$$ denotes the dimension. We also give related results concerning the integrability of the diameter of subcritical clusters.

##### MSC:
 60K35 Interacting random processes; statistical mechanics type models; percolation theory 60D05 Geometric probability and stochastic geometry 82B43 Percolation
##### Keywords:
continuum percolation; Poisson Boolean model
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##### References:
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