The Kardar-Parisi-Zhang equation and universality class

随机偏微分方程组(SPDE)在整个科学中被用来提供比 当存在随机性或不确定性时的偏微分方程组。然而，我们对这些的理解 方程式还处于初级阶段。调查员正在研究完全不属于该领域的相关例子。 对目前的理论进行总结，以期发展出一套适用的SPDE理论。最重要的例子是Kardar-Parisi-Zhang方程。尽管该方程在物理学中被广泛用于模拟随机增长的界面，但非常 关于适当性或解决方案是什么，人们知之甚少。在过去的几年里，调查员已经 发现了几个精确的解，本研究的目的是建立在这些解的基础上，并揭示 方程式。

Stochastic partial differential equations (SPDE) are used throughout the sciences to provide more precise models than partial differential equations when randomness or uncertainty are present. However, our understanding of these equation is in a primitive stage. The investigator is studying relevant examples which fall well out of the domain of present theory, in order to develop an applicable theory of SPDE. The most important example is the Kardar-Parisi-Zhang equation. Although the equation is widely used in physics to model randomly growing interfaces, very little was known about well-posedness, or what the solutions looked like. In the last few years, the investigator has discovered several exact solutions, and this research aims to build on these and uncover the integrable structure of the equation.