We consider the scalar field φt with a reversible stochastic dynamics which is defined by the standard Dirichlet form relative to the Gibbs measure with formal energy ∫ ddxV(▽φ(x)). The potential V is even and strictly convex. We prove that under a suitable large scale limit the φt-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.
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics