THE GAUSSIAN FREE-FIELD AS A STREAM FUNCTION: ASYMPTOTICS OF EFFECTIVE DIFFUSIVITY IN INFRA-RED CUT-OFF

• 成果类型: Article
• 署名作者: Chatzigeorgiou, Georgiana; Morfe, Peter; Otto, Felix; Wang, Lihan
• 署名单位: Max Planck Society
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/24-AOP1740
• 发表日期: 2025
• 页码: 1510-1536
• 关键词: CENTRAL-LIMIT-THEOREM; random-walks; invariance-principle; homogenization; superdiffusivity; stationary; degenerate

摘要

We analyze the large-time asymptotics of a passive tracer with drift equal to the curl of the Gaussian free field in two dimensions with ultra-violet cutoff at scale unity. We prove that the mean-squared displacement scales like t root lnt, as predicted in the physics literature. This improves the asymptotics recently established in recent work of Cannizzaro, Haunschmidt-Sibitz, and Toninelli (Ann. Probab. 50 (2022) 2475-2498), which uses mathematical-physics type analysis in Fock space. Our approach involves studying the effective diffusivity ) L of the process with an infra-red cut-off at scale L, and is based on techniques from stochastic homogenization.