Hydrodynamic Limit for the ∇φ Interface Model via Two-Scale Approach

Conference paper
Part of the Springer Proceedings in Mathematics book series (PROM, volume 11)

Abstract

We prove the hydrodynamic limit for the Ginzburg–Landau ∇φ interface model based on a two-scale approach recently introduced by Grunewald et al.6 under the assumptions of the strict convexity of the coarse-grained Hamiltonian and the logarithmic Sobolev inequality for canonical Gibbs measures. In particular, strictly convex potentials satisfy these assumptions.

Keywords

Gibbs Measure Dirichlet Form Interface Model Variational Formula Directed Bond 
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Notes

Acknowledgements

The author thanks Jean-Dominique Deuschel who suggested the method employed in Sect. 4.2.2.

References

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Graduate School of Mathematical SciencesUniversity of TokyoTokyoJapan

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