The parallel replica method for computing equilibrium averages of Markov chains

An algorithm is proposed for computing equilibrium averages of Markov chains which su er from metastability – the tendency to remain in one or more subsets of state space for long time intervals. The algorithm, called the parallel replica method (or ParRep), uses many parallel processors to explore these subsets more e ciently. Numerical simulations on a simplemodel demonstrate consistency of themethod. A proof of consistency is given in an idealized setting. The parallel replica method can be considered a generalization of A. F. Voter’s parallel replica dynamics, originally developed to e ciently simulate metastable Langevin stochastic dynamics.