Fluctuations of the solutions to the KPZ equation in dimensions three and higher

• 成果类型: Article
• 署名作者: Dunlap, Alexander; Gu, Yu; Ryzhik, Lenya; Zeitouni, Ofer
• 署名单位: Stanford University; Carnegie Mellon University; Weizmann Institute of Science
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-019-00938-w
• 发表日期: 2020
• 页码: 1217-1258
• 关键词: directed polymers; heat-equation; limit; UNIVERSALITY; diffusion

摘要

We prove, using probabilistic techniques and analysis on the Wiener space, that the large scale fluctuations of the KPZ equation in d >= 3 with a small coupling constant, driven by a white in time and colored in space noise, are given by the Edwards-Wilkinson model. This gives an alternative proof, that avoids perturbation expansions, to the results of Magnen and Unterberger (J Stat Phys 171:543-598, 2018).