A CENTRAL LIMIT THEOREM FOR THE KPZ EQUATION

• 成果类型: Article
• 署名作者: Hairer, Martin; Shen, Hao
• 署名单位: University of Warwick; University of Warwick; Columbia University
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/16-AOP1162
• 发表日期: 2017
• 页码: 4167-4221
• 关键词: regularity structures; particle-systems; RENORMALIZATION

摘要

We consider the KPZ equation in one space dimension driven by a stationary centred space-time random field, which is sufficiently integrable and mixing, but not necessarily Gaussian. We show that, in the weakly asymmetric regime, the solution to this equation considered at a suitable large scale and in a suitable reference frame converges to the Hopf-Cole solution to the KPZ equation driven by space-time Gaussian white noise. While the limiting process depends only on the integrated variance of the driving field, the diverging constants appearing in the definition of the reference frame also depend on higher order moments.