Existence of `nearest-neighbour spatial Gibbs models

The present study deals with the existence of `nearest-neighbourʹ type Gibbs models, introduced by Baddeley and Moller 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, Ordʹs model and Markov connected component type models.