Subcritical regimes in the Poisson Boolean model of continuum percolation

Abstract

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.