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Markos A. Katsoulakis, Petr Plechac. Luc Rey-Bellet, Dimitrios K. Tsagkarogannis

Coarse-graining schemes for stochastic lattice systems with short and long-range interactions

We develop coarse-graining schemes for stochastic many-particle microscopic models with competing short- and long-range interactions on a $d$-dimensional lattice. We focus on the coarse-graining of equilibrium Gibbs states and using cluster expansions we analyze the corresponding renormalization group map. We quantify the approximation properties of the coarse-grained terms arising from different types of interactions and present a hierarchy of correction terms. We derive semi-analytical numerical schemes that are accompanied with a posteriori error estimates for coarse-grained lattice systems with short and long-range interactions.

Bibliographical note:

submitted to Mathematics of Computation
preprint on arXiv: arXiv: 1003.1506 [math.NA]