### 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 ∫ d^{d}xV(▽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.

Original language | English |
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Pages (from-to) | 1-36 |

Number of pages | 36 |

Journal | Communications in Mathematical Physics |

Volume | 185 |

Issue number | 1 |

DOIs | |

Publication status | Published - 1997 Jan 1 |

Externally published | Yes |

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics

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## Cite this

Funaki, T., & Spohn, H. (1997). Motion by mean curvature from the Ginzburg-Landau ▽ φ interface model.

*Communications in Mathematical Physics*,*185*(1), 1-36. https://doi.org/10.1007/s002200050080