A note on the existence of Gibbs marked point processes with applications in stochastic geometry
This paper generalizes a recent existence result for infinite-volume marked Gibbs point processes. We try to use the existence theorem for two models from stochastic geometry. First, we show the existence of Gibbs facet processes in with repulsive interactions. We also prove that the finite-volume Gibbs facet processes with attractive interactions need not exist. Afterwards, we study Gibbs-Laguerre tessellations of . The mentioned existence result cannot be used, since one of its assumptions...