论文标题
排除过程和KPZ方程与KPZ固定点的收敛性
Convergence of exclusion processes and KPZ equation to the KPZ fixed point
论文作者
论文摘要
我们表明，在1：2：3缩放下，批判性地探测了大空间和时间，有限范围不对称排除过程的高度函数和KPZ方程收敛到KPZ固定点，以前构建为完全不对称的简单排除过程，通过精确的公式构建。 因此，基于\ cite {wu}，\ cite {dm20}的最新结果，kpz line集合收敛到通风线集合。 对于KPZ方程，我们可以从连续功能加上有限的狭窄楔子集合开始。对于最近的邻居排除，我们可以使用$ h（x）\ le c（1+ | x |）$的高度功能（离散化）。对于非最新邻居排除，目前我们被限制为一类（随机）初始数据，在紧凑型统一收敛的拓扑中的连续功能中密集。 该方法是通过比较有限范围排除过程的过渡概率和使用能量估计的完全不对称的简单排除过程。
We show that under the 1:2:3 scaling, critically probing large space and time, the height function of finite range asymmetric exclusion processes and the KPZ equation converge to the KPZ fixed point, constructed earlier as a limit of the totally asymmetric simple exclusion process through exact formulas. Consequently, based on recent results of \cite{wu},\cite{DM20}, the KPZ line ensemble converges to the Airy line ensemble. For the KPZ equation we are able to start from a continuous function plus a finite collection of narrow wedges. For nearest neighbour exclusions, we can take (discretizations) of height functions with $h(x)\le C(1+|x|)$. For non-nearest neighbour exclusions, we are restricted at the present time to a class of (random) initial data, dense in continuous functions in the topology of uniform convergence on compacts. The method is by comparison of the transition probabilities of finite range exclusion processes and the totally asymmetric simple exclusion processes using energy estimates.
