周期定向景观
Periodic directed landscape
浏览论文内容
中文总结 AI 辅助
研究构建周期定向景观，证明周期指数最后通过渗流及周期非对称简单排斥过程向其收敛，证实关于周期 KPZ 不动点局部结构的猜想，主要工具是粘合全空间定向景观的技术。
中文摘要 AI 辅助
我们构建了周期定向景观，它是 Kardar-Parisi-Zhang 普适类中周期模型的推测标度极限。我们证明了周期指数最后通过渗流收敛到周期定向景观。此外，我们证实了 Baik、Liao 和 Liu 关于周期 KPZ 不动点局部结构的猜想，并证明了周期非对称简单排斥过程收敛到根据相同周期定向景观耦合的周期 KPZ 不动点。我们构建周期定向景观（并证明向其收敛）的主要工具是一种粘合全空间定向景观（及其预极限）的技术，该技术具有独立的研究价值。
英文摘要
We construct the periodic directed landscape, which is the conjectured scaling limit for periodic models in the Kardar-Parisi-Zhang universality class. We establish the convergence of periodic exponential last passage percolation to the periodic directed landscape. Moreover, we confirm conjectures by Baik, Liao and Liu on the local structure of the periodic KPZ fixed point, and establish the convergence of periodic ASEPs to periodic KPZ fixed points, coupled according to the same periodic directed landscape. Our main tool to construct the periodic directed landscape (and prove convergence to it) is a technique for gluing full-space directed landscapes (and their prelimits), which is of independent interest.
