Motion by Mean Curvature from the Ginzburg-Landau
Interface Model |
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Authors: | T Funaki H Spohn |
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Institution: | Department of Mathematical Sciences, University of Tokyo, 3-8-1 Komaba, Meguro, Tokyo, 153 Japan. E-mail: funaki@ms.u-tokyo.ac.jp, JP Theoretische Physik, Ludwig-Maximilians-Universit?t, Theresienstr. 37, D-80333 München, Germany.?E-mail: spohn@stat.physik.uni-muenchen.de, DE
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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.
Received: 1 February 1996 / Accepted: 2 July 1996 |
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Keywords: | |
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