Fluctuations for ∇φ interface model on a wall

Tadahisa Funaki*, Stefano Olla

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

53 Citations (Scopus)


We consider ∇φ interface model on a hard wall. The hydrodynamic large-scale space-time limit for this model is discussed with periodic boundary by Funaki et al. (2000, preprint). This paper studies fluctuations of the height variables around the hydrodynamic limit in equilibrium in one dimension imposing Dirichlet boundary conditions. The fluctuation is non-Gaussian when the macroscopic interface is attached to the wall, while it is asymptotically Gaussian when the macroscopic interface stays away from the wall. Our basic method is the penalization. Namely, we substitute in the dynamics the reflection at the wall by strong drift for the interface when it goes down beyond the wall and show the fluctuation result for such massive ∇φ interface model. Then, this is applied to prove the fluctuation for the ∇φ interface model on the wall.

Original languageEnglish
Pages (from-to)1-27
Number of pages27
JournalStochastic Processes and their Applications
Issue number1
Publication statusPublished - 2001 Jul
Externally publishedYes


  • Entropic repulsion
  • Equilibrium fluctuations
  • Hard wall
  • Interface model
  • Primary 60K35
  • Secondary 82A05
  • Stochastic partial differential equations

ASJC Scopus subject areas

  • Statistics and Probability
  • Modelling and Simulation
  • Applied Mathematics


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