论文标题
高斯自由场作为流函数：在红外截止中有效扩散率的渐近学
The Gaussian free-field as a stream function: asymptotics of effective diffusivity in infra-red cut-off
论文作者
论文摘要
我们分析了一个被动示踪剂的大渐近造物分析，其漂移等于在统一的统一的超紫罗兰截止的二维中等于高斯自由场的卷发。我们证明，如物理学文献所预测的那样，均方体位移量表如$ t \ sqrt {\ ln t} $，最近几乎是由Cannizzaro，Cannizzaro，Haunschmidt-Sibitz和Toninelli（2022）（2022）的工作证明的，该工作使用了fock Space在Fock Space中使用Mathematical-Physics类型。我们的方法涉及研究该过程的有效扩散性$λ_{l} $，并以规模$ l $的标准截止截止数量，并基于随机均质化的技术。
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 cut-off at scale unity. We prove that the mean-squared displacement scales like $t \sqrt{\ln t}$, as predicted in the physics literature and recently almost proved by the work of Cannizzaro, Haunschmidt-Sibitz, and Toninelli (2022), which uses mathematical-physics type analysis in Fock space. Our approach involves studying the effective diffusivity $λ_{L}$ of the process with an infra-red cut-off at scale $L$, and is based on techniques from stochastic homogenization.
