FLUCTUATIONS OF PARTITION FUNCTIONS OF DIRECTED POLYMERS IN WEAK DISORDER BEYOND THE L2-PHASE

• 成果类型: Article
• 署名作者: Tunk, Stefan
• 署名单位: Gakushuin University
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/24-AOP1716
• 发表日期: 2025
• 页码: 557-596
• 关键词: diffusion; equation; limit

摘要

We study the directed polymer model in a bounded environment in weak disorder without L2-boundedness, specifically the speed of homogenization for the field (Wnx)xEZd, where Wnxdenotes the associated martingale for the polymer starting from x. We show that a suitably recentered spatial average over a set of diameter n1/2 convergence to zero at rate n-xi+o(1), where the exponent is an explicit function of the inverse temperature beta.