We study computational aspects of repulsive Gibbs point processes, which are probabilistic models of interacting particles in a finite-volume region of space. We introduce an approach for reducing a Gibbs point process to the hard-core model, a well-studied discrete spin system. Given an instance of such a point process, our reduction generates a random graph drawn from a natural geometric model. We show that the partition function of a hard-core model on graphs generated by the geometric model concentrates around the partition function of the Gibbs point process. Our reduction allows us to use a broad range of algorithms developed for the hard-core model to sample from the Gibbs point process and approximate its partition function. This is, to the extent of our knowledge, the first approach that deals with pair potentials of unbounded range.

The present study deals with the existence of ‘nearest-neighbour’ type Gibbs models, introduced by Baddeley and Møller in 1989. In such models, the neighbourhood relation depends on the realization of the process. After giving new sufficient conditions to prove the existence of stationary Gibbs states, we deal with the first-nearest-neighbour model, the triplets Delaunay model, Ord's model and Markov connected component type models.