Existence of ‘nearest-neighbour’ spatial Gibbs models

Abstract

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.