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Error control and analysis in coarse-graining of stochastic lattice dynamics

The coarse-grained Monte Carlo (CGMC) algorithm was originally proposed in the series of works [15, 16]. In this paper we further investigate the approximation properties of the coarse-graining procedure and relation between the coarse-grained and microscopic processes. We provide both analytical and numerical evidence that the hierarchy of the coarse models is built in a systematic way that allows for the error control of quantities that may also depend on the path. We also demonstrate that CGMC leads to a significant CPU speed-up of simulations of metastable phenomena, e.g., estimation of switching times or nucleation of new phases. Numerical evidence guided by analytical results suggests that CGMC probes the energy landscape in path-wise agreement to MC simulations at the microscopic level.