Continuum percolation for Gibbs point processes

Kaspar Stucki

Published 2013-05-02, updated 2013-08-09Version 2

We consider percolation properties of the Boolean model generated by a Gibbs point process and balls with deterministic radius. We show that for a large class of Gibbs point processes there exists a critical activity, such that percolation occurs a.s. above criticality. For locally stable Gibbs point processes we show a converse result, i.e. they do not percolate a.s. at low activity.