论文标题
关于随机汉堡方程的能源解决方案
On energy solutions to stochastic Burgers equation
论文作者
论文摘要
在这篇综述中，我们讨论了一类动力学能够保守一个或多个数量的1-D系统的KPZ普遍性较弱的猜想。作为前一种情况的原型示例，我们将重点放在弱的不对称简单排除过程上，为此，保留了密度，并且显示平衡波动从Edwards-Wilkinson普遍性类别跨越KPZ普遍性类别。交叉取决于不对称的强度。对于后一种情况，我们将提出一个排除过程，其中包含三种颗粒（称为ABC模型），我们的目的是证明与耦合随机汉堡方程系统的收敛性，即耦合KPZ方程的梯度版本。我们将回顾有关此问题的最新结果，围绕[26]中引入的能源解决方案的概念，在[35]中证明了唯一性。
In this review we discuss the weak KPZ universality conjecture for a class of 1-d systems whose dynamics conserves one or more quantities. As a prototype example for the former case, we will focus on weakly asymmetric simple exclusion processes, for which the density is preserved and the equilibrium fluctuations are shown to cross from the Edwards-Wilkinson universality class to the KPZ universality class. The crossover depends on the strength of the asymmetry. For the latter case, we will present an exclusion process with three species of particles, known as the ABC model, for which we aim to prove the convergence to a system of coupled stochastic Burgers' equations, i.e. gradient versions of coupled KPZ equations. We will review the recent results on this matter around the notion of energy solutions introduced in [26] for which uniqueness has been proved in [35].
