Abstract:
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 . 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 -field.
Similar content being viewed by others
Author information
Authors and Affiliations
Additional information
Received: 1 February 1996 / Accepted: 2 July 1996
Rights and permissions
About this article
Cite this article
Funaki, T., Spohn, H. Motion by Mean Curvature from the Ginzburg-Landau Interface Model . Comm Math Phys 185, 1–36 (1997). https://doi.org/10.1007/s002200050080
Issue Date:
DOI: https://doi.org/10.1007/s002200050080