On Large Deviations of Interface Motions for Statistical Mechanics Models

We discuss the sharp interface limit of the action functional associated with either the Glauber dynamics for Ising systems with Kac potentials or the Glauber+Kawasaki process. The corresponding limiting functionals, for which we provide explicit formulae of the mobility and transport coefficients, describe the large deviation asymptotics with respect to the mean curvature flow.