We study the probability of the macroscopic motion of an interface between
two stable phases of a ferromagnetic system from an initial to a final
position within fixed macroscopic time. We work with a stochastic microscopic
system of Ising spins with Kac interaction evolving in time according to
the Glauber (non-conservative) dynamics. We derive the cost functional
penalizing all possible transitions and we minimize it to find the most
probable profile which corresponds to the motion of the interface in the
macroscopic scale. This is joint work with N. Dirr and G. Manzi.