Directed polymers in random environment are diffusive at weak disorder

• 成果类型: Article
• 署名作者: Comets, Francis; Yoshida, Nobuo
• 署名单位: Universite Paris Cite; Kyoto University
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/009117905000000828
• 发表日期: 2006
• 页码: 1746-1770
• 关键词: fluctuations

摘要

In this paper we consider directed polymers in random environment with discrete space and time. For transverse dimension at least equal to 3, we prove that diffusivity holds for the path in the full weak disorder region, that is, where the partition function differs from its annealed value only by a non-vanishing factor. Deep inside this region, we also show that the quenched averaged energy has fluctuations of order 1. In complete generality (arbitrary dimension and temperature), we prove monotonicity of the phase diagram in the temperature.