Coarse-graining schemes for stochastic lattice systems

In this talk we present a method to construct higher order Monte Caro numerical schemes for the coarse-graining of stochastic lattice systems with short and long range interactions. The main tool is the cluster expansion of the partition function of the conditioned (to the coarse-grained variables) measure. We also discuss a strategy on how to recover microscopic information from the coarse-grained one.