Fluctuations for ∇φ interface model on a wall

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.