论文标题
$ t $ -PNG模型的流体动力学通过彩色$ t $ -png型号
Hydrodynamics of the $t$-PNG model via a colored $t$-PNG model
论文作者
论文摘要
在Aggarwal，Borodin和Wheeler（2021）中引入的$ T $ -PNG模型是多核增长（PNG）模型的变形版。在本文中，我们使用软技术证明了模型的流体动力极限。证明的一个关键要素是构建$ t $ -PNG型号的彩色版本，该版本使我们能够应用超脱脂的ergodic定理并获得流体动力限制，尽管不识别限制常数。然后，我们通过证明$α$点的大量法律来发现这个常数，该法律概括了Groeneboom（2001）。一路上，我们构建了固定的$ t $ -png型号，并证明了Burke的定理版本。
The $t$-PNG model introduced in Aggarwal, Borodin, and Wheeler (2021) is a deformed version of the polynuclear growth (PNG) model. In this paper, we prove the hydrodynamic limit of the model using soft techniques. One key element of the proof is the construction of a colored version of the $t$-PNG model, which allows us to apply the superadditive ergodic theorem and obtain the hydrodynamic limit, albeit without identifying the limiting constant. We then find this constant by proving a law of large numbers for the $α$-points, which generalizes Groeneboom (2001). Along the way, we construct the stationary $t$-PNG model and prove a version of Burke's theorem for it.
