论文标题
开放式ASEP上非简单变化的KPZ方程
KPZ Equation from non-simple variations on open ASEP
论文作者
论文摘要
本文有两个主要目标。首先是KPZ方程的通用性，用于在存在开放边界的情况下与相互作用粒子系统相关的动态接口的波动。我们考虑[Corwin-Shen '16，Parekh '17]对开放式的概括，但在边界和大部分粒子系统内都承认非简单相互作用。开放式ABASEP上的这些变化不是可集成的模型，类似于[Dembo-Tsai '15，Y '20]中考虑的ASEP的远程变化。我们建立具有适当的罗宾边界条件的KPZ方程，作为与这些不可积分模型相关的高度函数波动的缩放限制，为KPZ方程的上述普遍性提供了进一步的证据。我们专注于紧凑型域并在第二篇论文中解决非紧凑型域。我们采用的确定上述定理的程序是本文的第二个要点。在存在边界相互作用的情况下，不变的度量通常缺乏合理的描述。因此，通过不变措施进行的全球分析，包括[Goncalves-Jara '14，Goncalves-Jara '17，Goncalves-Jara-Jara-Sethuraman '15]中的能量解决方案理论。为了避免这种障碍，我们在[Y '20]中呼吁分析的几乎完全局部性质。
This paper has two main goals. The first is universality of the KPZ equation for fluctuations of dynamic interfaces associated to interacting particle systems in the presence of open boundary. We consider generalizations on the open-ASEP from [Corwin-Shen '16, Parekh '17] but admitting non-simple interactions both at the boundary and within the bulk of the particle system. These variations on open-ASEP are not integrable models, similar to the long-range variations on ASEP considered in [Dembo-Tsai '15, Y '20]. We establish the KPZ equation with the appropriate Robin boundary conditions as scaling limits for height function fluctuations associated to these non-integrable models, providing further evidence for the aforementioned universality of the KPZ equation. We specialize to compact domains and address non-compact domains in a second paper. The procedure that we employ to establish the aforementioned theorem is the second main point of this paper. Invariant measures in the presence of boundary interactions generally lack reasonable descriptions. Thus, global analyses done through the invariant measure, including the theory of energy solutions in [Goncalves-Jara '14, Goncalves-Jara '17, Goncalves-Jara-Sethuraman '15], is immediately obstructed. To circumvent this obstruction, we appeal to the almost entirely local nature of the analysis in [Y '20].
