### 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 |
---|---|

Pages (from-to) | 1-36 |

Number of pages | 36 |

Journal | Communications in Mathematical Physics |

Volume | 185 |

Issue number | 1 |

Publication status | Published - 1997 |

Externally published | Yes |

### Fingerprint

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics

### Cite this

*Communications in Mathematical Physics*,

*185*(1), 1-36.

**Motion by mean curvature from the Ginzburg-Landau ▽ φ interface model.** / Funaki, Tadahisa; Spohn, H.

Research output: Contribution to journal › Article

*Communications in Mathematical Physics*, vol. 185, no. 1, pp. 1-36.

}

TY - JOUR

T1 - Motion by mean curvature from the Ginzburg-Landau ▽ φ interface model

AU - Funaki, Tadahisa

AU - Spohn, H.

PY - 1997

Y1 - 1997

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0002088207&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0002088207&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0002088207

VL - 185

SP - 1

EP - 36

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

SN - 0010-3616

IS - 1

ER -