论文标题
KPZ通用类中的可整合波动
Integrable fluctuations in the KPZ universality class
论文作者
论文摘要
KPZ固定点是一个扩展不变的马尔可夫过程，它是一维界面增长的广泛模型的通用缩放限制，即一维KPZ通用类别。在本调查中，我们回顾了KPZ固定点的构建以及导致它的一些历史，尤其是通过完全不对称的简单排除过程的精确解决方案，这是同类产品中的一种特殊可解决的模型。我们还解释了该结构如何将KPZ固定点作为随机集成系统揭示，以及从中如何得出的有限尺寸分布满足了经典的可集成色散PDE，即Kadomtsev-PetviaShvili（KP）方程。
The KPZ fixed point is a scaling invariant Markov process which arises as the universal scaling limit of a broad class of models of random interface growth in one dimension, the one-dimensional KPZ universality class. In this survey we review the construction of the KPZ fixed point and some of the history that led to it, in particular through the exact solution of the totally asymmetric simple exclusion process, a special solvable model in the class. We also explain how the construction reveals the KPZ fixed point as a stochastic integrable system, and how from this it follows that its finite dimensional distributions satisfy a classical integrable dispersive PDE, the Kadomtsev-Petviashvili (KP) equation.
