论文标题
固定kardar-parisi-zhang方程的老化和相关模型
Aging for the stationary Kardar-Parisi-Zhang equation and related models
论文作者
论文摘要
我们研究KPZ通用类中固定模型的老化特性。特别是，我们显示了固定KPZ固定点的老化，固定KPZ方程的Cole-HOPF解决方案，固定tasep的高度功能，最后一个通用的渗透，具有边界条件和中等疾病状态中的固定定向聚合物。所有这些模型均显示出表现出以其相关性衰减速率为特征的普遍衰老行为。作为比较，我们显示了在Edwards-Wilkinson普遍性类别中获得不同衰减指数的模型的老化。我们证明的关键要素是时空平稳性的特征 - 协方差 - 变化降低 - 允许一个方差之一推断两个时空点的相关性的渐近行为。我们提出了几个开放问题。
We study the aging property for stationary models in the KPZ universality class. In particular, we show aging for the stationary KPZ fixed point, the Cole-Hopf solution to the stationary KPZ equation, the height function of the stationary TASEP, last-passage percolation with boundary conditions and stationary directed polymers in the intermediate disorder regime. All of these models are shown to display a universal aging behavior characterized by the rate of decay of their correlations. As a comparison, we show aging for models in the Edwards-Wilkinson universality class where a different decay exponent is obtained. A key ingredient to our proofs is a characteristic of space-time stationarity - covariance-to-variance reduction - which allows to deduce the asymptotic behavior of the correlations of two space-time points by the one of the variances at one point. We formulate several open problems.
