GENERALIZED MOTION BY MEAN-CURVATURE AS A MACROSCOPIC LIMIT OF STOCHASTIC ISING-MODELS WITH LONG-RANGE INTERACTIONS AND GLAUBER DYNAMICS

We study the macroscopic limit Of an appropriately rescaled stochastic Ising model with long range interactions evolving with Glauber dynami cs as well as the corresponding mean field equation, which is nonlinea r and nonlocal. in the limit we obtain an interface evolving with norm al velocity theta kappa, where kappa is the mean curcature and the tra nsport coefficient theta is identified by an effective Green-Kubo type formula. The above assertions are valid for all positive times, the m otion of the interface being interpreted in the viscosity sense after the onset of the geometric singularities.