Let ηt be a Poisson point process of intensity t≥1 on some state space Y and let f be a non-negative symmetric function on Yk for some k≥1. Applying f to all k-tuples of distinct points of ηt generates a point process ξt on the positive real half-axis. The scaling limit of ξt as t tends...

We introduce a class of Gibbs-Markov random fields built on regular tessellations that can be understood as discrete counterparts of Arak-Surgailis polygonal fields. We focus first on consistent polygonal fields, for which we show consistency, Markovianity and solvability by means of dynamic...