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We study the stochastic motion of a droplet in a stochastic Cahn-Hilliardequation in the sharp interface limit for sufficiently small noise. The keyingredient in the proof is a deterministic slow manifold, where we show itsstability for long times under small stochastic perturbations. We also give arigorous stochastic differential equation for the motion of the center of thedroplet.

Stochastic Cahn-Hilliard equation in higher space dimensions: The motion of bubbles