Subcritical regimes in some models of continuum percolation

Abstract

We consider some continuum percolation models. We are mainly interested in giving some sufficient conditions for the absence of percolation. We give some general conditions and then focus on two examples. The first one is a multiscale percolation model based on the Boolean model. It was introduced by Meester and Roy and subsequently studied by Menshikov, Popov and Vachkovskaia. The second one is based on the stable marriage of Poisson and Lebesgue introduced by Hoffman, Holroyd and Peres and whose percolation properties have been studied by Freire, Popov and Vachkovskaia.