Perkolation auf zufälligen Mosaiken und im Boole\u27schen Modell

We study percolation on random tessellations of the euclidian space. We proof the uniqueness of the infinite cluster and provide two frameworks, that imply the existence of a non-trivial phase-transition. We show that various classes of random tesselations fit into on of these frameworks. In the second part, we study the Boolean model. We give a new proof for the sharpness of the phase transition and solve the Ornstein-Zernike equation. This leads to new lower bounds for the critical intensity