Perfect sampling for Gibbs point processes using partial rejection sampling

We present a perfect sampling algorithm for Gibbs point processes, based on the partial rejection sampling of Guo, Jerrum and Liu (In STOC'17 - Proceedings of the 49th Annual ACM SIGACT Symposium on Theory of Computing (2017) 342-355 ACM). Our particular focus is on pairwise interaction processes, penetrable spheres mixture models and area-interaction processes, with a finite interaction range. For an interaction range 2r of the target process, the proposed algorithm can generate a perfect sample with O(log(1/r)) expected running time complexity, provided that the intensity of the points is not too high and circle minus(1/r(d)) parallel processor units are available