MAXIMUM AND ENTROPIC REPULSION FOR A GAUSSIAN MEMBRANE MODEL IN THE CRITICAL DIMENSION

• 成果类型: Article
• 署名作者: Kurt, Noemi
• 署名单位: University of Zurich
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/08-AOP417
• 发表日期: 2009
• 页码: 687-725
• 关键词: free-field; interface

摘要

We consider the real-valued centered Gaussian field on the four-dimensional integer lattice, whose covariance matrix is given by the Green's function of the discrete Bilaplacian. This is interpreted as a model for a semi-flexible membrane. d = 4 is the critical dimension for this model. We discuss the effect of a hard wall on the membrane, via a multiscale analysis of the maximum of the field. We use analytic and probabilistic tools to describe the correlation structure of the field.