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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
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