Motion by mean curvature from the Ginzburg-Landau ▽ φ interface model

We consider the scalar field φ_t with a reversible stochastic dynamics which is defined by the standard Dirichlet form relative to the Gibbs measure with formal energy ∫ d^dxV(▽φ(x)). The potential V is even and strictly convex. We prove that under a suitable large scale limit the φ_t-field becomes deterministic such that locally its normal velocity is proportional to its mean curvature, except for some anisotropy effects. As an essential input we prove that for every tilt there is a unique shift invariant, ergodic Gibbs measure for the ▽φ-field.