KPZ EQUATION CORRELATIONS IN TIME

• 成果类型: Article
• 署名作者: Corwin, Ivan; Ghosal, Promit; Hammond, Alan
• 署名单位: Columbia University; Massachusetts Institute of Technology (MIT); University of California System; University of California Berkeley; University of California System; University of California Berkeley
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/20-AOP1461
• 发表日期: 2021
• 页码: 832-876
• 关键词: directed polymers; fluctuations; distributions; UNIVERSALITY

摘要

We consider the narrow wedge solution to the Kardar-Parisi-Zhang stochastic PDE under the characteristic 3 : 2 : 1 scaling of time, space and fluctuations. We study the correlation of fluctuations at two different times. We show that, when the times are close to each other, the correlation approaches one at a power-law rate with exponent 2/3, while, when the two times are remote from each other, the correlation tends to zero at a powerlaw rate with exponent -1/3. We also prove exponential-type tail bounds for differences of the solution at two space-time points. Three main tools are pivotal to proving these results: (1) a representation for the two-time distribution in terms of two independent narrow wedge solutions, (2) the Brownian Gibbs property of the KPZ line ensemble and (3) recently proved one-point tail bounds on the narrow wedge solution.