Characterization results and Markov chain Monte Carlo algorithms includingexact simulation for some spatial point processes

The area-interaction process and the continuum random-duster model are char acterized in terms of certain functional forms of their respective conditio nal intensities. In certain cases, these two point process models can be de rived from a bivariate point process model which in many respects is simple r to analyse and simulate. Using this correspondence we devise a two-compon ent Gibbs sampler, which can be used for fast and exact simulation by exten ding the recent ideas of Propp and Wilson. We further introduce a Swendsen- Wang type algorithm. The relevance of the results within spatial statistics :as well as statistical physics is discussed.