Ever increasing computational power along with ever more sophisticated statistical computing techniques is making it possible to fit ever more complex statistical models. Among the popular, computationally intensive methods, the Gibbs sampler (Geman and Geman, 1984) has been spotlighted because of its simplicity and power to effectively generate samples from a high-dimensional probability distr...

Given a countable graph G and a finite graph H, we consider Hom(G ,H) the set of graph homomorphisms from G to H and we study Gibbs measures supported on Hom(G ,H). We develop some sufficient and other necessary conditions on Hom(G ,H) for the existence of Gibbs specifications satisfying strong spatial mixing (with exponential decay rate). We relate this with previous work of Brightwell and Win...