Fluctuations for a delφ interface model with repulsion from a wall

• 成果类型: Article
• 署名作者: Zambotti, L
• 署名单位: Scuola Normale Superiore di Pisa; University of Bielefeld
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-004-0335-1
• 发表日期: 2004
• 页码: 315-339
• 关键词: integration; spdes; parts

摘要

We consider a delphi interface model on a one-dimensional lattice with repulsion from a hard wall. We suppose that the repulsion is of the form cphi(-alpha-1), where c,alpha>0 and phi 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 delphi 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.