Localization in log-gamma polymers with boundaries

• 成果类型: Article
• 署名作者: Comets, Francis; Vu-Lan Nguyen
• 署名单位: Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Sorbonne Universite; Universite Paris Cite
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-015-0662-4
• 发表日期: 2016
• 页码: 429-461
• 关键词: directed polymers; random-walks; random environment; partition-function; DECOMPOSITION; diffusion; infimum

摘要

Consider the directed polymer in one space dimension in log-gamma environment with boundary conditions, introduced by Seppalainen (Ann Probab, 40(1):19-73, 2012). In the equilibrium case, we prove that the end point of the polymer converges in law as the length increases, to a density proportional to the exponent of a zero-mean random walk. This holds without space normalization, and the mass concentrates in a neighborhood of the minimum of this random walk. We have analogous results out of equilibrium as well as for the middle point of the polymer with both ends fixed. The existence and the identification of the limit relies on the analysis of a random walk seen from its infimum.