论文标题
热量和景观
The heat and the landscape I
论文作者
论文摘要
缩放到定向景观描述的随机几何形状后，热流在1+1维的随机环境中会收敛。在第一部分中，我们表明O'Connell-Yor聚合物和KPZ方程会收敛到KPZ固定点。 关键是一维Baik-ben唤醒 - 彼得统计的特征是KPZ固定点。这产生了一种一般和基本方法，该方法根据先前确定的限制定理显示收敛性。 独立地，与此同时，Quastel和Sharkar提供了KPZ收敛的无关证明。这些方法邀请了不同方向的扩展：我们的聚合物模型及其对相互作用的粒子系统的扩展。
Heat flows in 1+1 dimensional stochastic environment converge after scaling to the random geometry described by the directed landscape. In this first part, we show that the O'Connell-Yor polymer and the KPZ equation converge to the KPZ fixed point. The key is that one-dimensional Baik-Ben Arous-Peche statistics characterize the KPZ fixed point. This yields a general and elementary method that shows convergence based on previously established limit theorems. Independently, at the same time and place Quastel and Sharkar gave an unrelated proof of KPZ convergence. The methods invite extensions in different directions: ours to polymer models, and theirs to interacting particle systems.
