Concentration under scaling limits for weakly pinned Gaussian random walks

• 成果类型: Article
• 署名作者: Bolthausen, Erwin; Funaki, Tadahisa; Otobe, Tatsushi
• 署名单位: University of Tokyo; University of Zurich
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-007-0132-8
• 发表日期: 2009
• 页码: 441-480
• 关键词: wetting models; (1+1)-dimension; inequalities; transition/; BEHAVIOR; fkg

摘要

We study scaling limits for d-dimensional Gaussian random walks perturbed by an attractive force toward a certain subspace of R-d, especially under the critical situation that the rate functional of the corresponding large deviation principle admits two minimizers. We obtain different type of limits, in a positive recurrent regime, depending on the co-dimension of the subspace and the conditions imposed at the final time under the presence or absence of a wall. The motivation comes from the study of polymers or (1 + 1)-dimensional interfaces with delta-pinning.