UNIVERSALITY OF DIRECTED POLYMERS IN THE INTERMEDIATE DISORDER REGIME

• 成果类型: Article
• 署名作者: Ransford, Julian
• 署名单位: University of Toronto
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/24-AOP1724
• 发表日期: 2025
• 页码: 1019-1048
• 关键词: log-gamma polymer; fluctuations

摘要

Krishnan and Quastel (Ann. Appl. Probab. 28 (2018) 3736-3764) showed that the fluctuations of Sepp & auml;l & auml;inen's log-gamma polymer converge in law to the Tracy-Widom GUE distribution in the intermediate disorder regime. This regime corresponds to taking the inverse temperature beta to depend on the length of the polymer 2n, with beta = n(-alpha) for some alpha < 1/4. They also conjectured that this should hold for directed polymers with general i.i.d weights. We prove that their conjecture is true for any 1/5 < alpha < 1/4.