Spatial Point Processes

Markov chain Monte Carlo (MCMC) originated with the classic paper of Metropolis et al. (1953), where it was used to simulate the distribution of states for a system of idealized molecules. Not long after, another approach tomolecular simulationwas introduced (Alder and Wainwright, 1959), in which the motion of the molecules was deterministic, following Newton’s laws ofmotion,which have an elegant formalization asHamiltonian dynamics. For finding the properties of bulk materials, these approaches are asymptotically equivalent, since even in a deterministic simulation, each local region of the material experiences effectively random influences from distant regions. Despite the large overlap in their application…