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.
"Continuum percolation for Gibbs point processes." Electron. Commun. Probab. 18 1 - 10, 2013. https://doi.org/10.1214/ECP.v18-2837