  We study the stochastic motion of a droplet in a stochastic Cahn-Hilliard
equation in the sharp interface limit for sufficiently small noise. The key
ingredient in the proof is a deterministic slow manifold, where we show its
stability for long times under small stochastic perturbations. We also give a
rigorous stochastic differential equation for the motion of the center of the
droplet.

Dynamical Systems;Analysis of PDEs;Probability