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Fluctuations for a ∇φ interface model with repulsion from a wall
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  • Published: 29 April 2004

Fluctuations for a ∇φ interface model with repulsion from a wall

  • Lorenzo Zambotti1 

Probability Theory and Related Fields volume 129, pages 315–339 (2004)Cite this article

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Abstract.

We consider a ∇φ interface model on a one-dimensional lattice with repulsion from a hard wall. We suppose that the repulsion is of the form cφ−α−1, where c,α>0 and φ denotes the height of the interface from the wall. We prove convergence of the equilibrium fluctuations around the hydrodynamic limit to the solution of a SPDE with singular drift. If c→0 the system becomes the Funaki-Olla ∇φ interface model with reflection at the wall, whose equilibrium fluctuations converge to the solution of a SPDE with reflection. We give a new proof of this result using the characterization of such solution as the diffusion generated by an infinite dimensional Dirichlet Form, obtained in a previous paper. Our method is based on a study of integration by parts formulae w.r.t. the equilibrium measure of the interface model and allows to avoid the proof of the so called Boltzmann-Gibbs principle. We also obtain convergence of finite dimensional distributions of non-equilibrium fluctuations around the stationary hydrodynamic limit 0.

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Authors and Affiliations

  1. Fakultät für Mathematik, Scuola Normale Superiore, Universität Bielefeld, Piazza dei Cavalieri 7, 56126, Pisa, 33501, Bielefeld, Germany/Italy

    Lorenzo Zambotti

Authors
  1. Lorenzo Zambotti
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Correspondence to Lorenzo Zambotti.

Additional information

This work has been supported by a Marie Curie Fellowship of the European Community programme IHP under contract number HPMF-CT-2002-01568.

Mathematics Subject Classification (2000):Primary 60K35, 60H15. Secondary 82B24, 82B41

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Zambotti, L. Fluctuations for a ∇φ interface model with repulsion from a wall. Probab. Theory Relat. Fields 129, 315–339 (2004). https://doi.org/10.1007/s00440-004-0335-1

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  • Received: 04 June 2003

  • Revised: 06 January 2004

  • Published: 29 April 2004

  • Issue Date: July 2004

  • DOI: https://doi.org/10.1007/s00440-004-0335-1

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Keywords

  • Equilibrium fluctuations
  • Interface model
  • Stochastic Partial Differential Equations
  • Integration by Parts
  • Dirichlet Forms
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