THERMODYNAMIC AND SCALING LIMITS OF THE NON-GAUSSIAN MEMBRANE MODEL

• 成果类型: Article
• 署名作者: Thoma, Eric
• 署名单位: New York University
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/22-AOP1609
• 发表日期: 2023
• 页码: 626-664
• 关键词: entropic repulsion; brunn-minkowski; maximum

摘要

We characterize the behavior of a random discrete interface phi on [-L, L](d) boolean AND Z(d) with energy Sigma V (Delta phi(x)) as L -> infinity, where Delta is the discrete Laplacian and V is a uniformly convex, symmetric, and smooth potential. The interface phi is called the non-Gaussian membrane model. By analyzing the Helffer-Sjostrand representation, associated to Delta phi, we provide a unified approach to continuous scaling limits of the rescaled and interpolated inter-face in dimensions d = 2, 3, Gaussian approximation in negative regularity spaces for all d >= 2, and the infinite volume limit in d >= 5.