Physical Sciences and Mathematics Commons^™

Coarse-Graining Schemes And A Posteriori Error Estimates For Stochastic Lattice Systems, Ma Katsoulakis, P Plechac, L Rey-Bellet, Dk Tsagkarogiannis

Luc Rey-Bellet

The primary objective of this work is to develop coarse-graining schemes for stochastic many-body microscopic models and quantify their effectiveness in terms of a priori and a posteriori error analysis. In this paper we focus on stochastic lattice systems of interacting particles at equilibrium. The proposed algorithms are derived from an initial coarse-grained approximation that is directly computable by Monte Carlo simulations, and the corresponding numerical error is calculated using the specific relative entropy between the exact and approximate coarse-grained equilibrium measures. Subsequently we carry out a cluster expansion around this first – and often inadequate – approximation and obtain …