Equilibrium fluctuations for ∇φ interface model

Giambattista Giacomin, Stefano Olla, Herbert Spohn

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76 Scopus citations


We study the large scale space-time fluctuations of an interface which is modeled by a massless scalar field with reversible Langevin dynamics. For a strictly convex interaction potential we prove that on a large space-time scale these fluctuations are governed by an infinite-dimensional Ornstein-Uhlenbeck process. Its effective diffusion type covariance matrix is characterized through a variational formula.

Original languageEnglish
Pages (from-to)1138-1172
Number of pages35
JournalAnnals of Probability
Issue number3
StatePublished - Jul 2001


  • De Giorgi-Nash-Moser and Aronson estimates
  • Equilibrium fluctuations
  • Gibbs measures
  • Homogenization
  • Interface model
  • Langevin dynamics
  • Massless field


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