论文标题
两周期AZTEC钻石中粗滑的界面的局部几何形状
Local Geometry of the rough-smooth interface in the two-periodic Aztec diamond
论文作者
论文摘要
两周期阿兹台克钻石的随机瓷砖包含三个宏观区域：冷冻，瓷砖是确定性的；粗糙，多米诺骨牌之间的相关性多一级衰减；平滑，在多米诺骨牌之间的相关性呈指数衰减。在上一篇论文中，作者发现，在粗糙平滑界面上的高度函数差异的一定平均值收敛到扩展的通风核点过程。在本文中，我们通过引入与高度函数的级别线密切相关的定义明确的晶格路径来增强本接口处的本地几何图片。我们表明，经过适当的居中和重新缩放，这些路径的点过程会收敛到扩展的通风内核点过程，但规定与两期周期性AZTEC钻石相关的自然参数足够小。
Random tilings of the two-periodic Aztec diamond contain three macroscopic regions: frozen, where the tilings are deterministic; rough, where the correlations between dominoes decay polynomially; smooth, where the correlations between dominoes decay exponentially. In a previous paper, the authors found that a certain averaging of height function differences at the rough-smooth interface converged to the extended Airy kernel point process. In this paper, we augment the local geometrical picture at this interface by introducing well-defined lattice paths which are closely related to the level lines of the height function. We show, after suitable centering and rescaling, that a point process from these paths converges to the extended Airy kernel point process provided that the natural parameter associated to the two-periodic Aztec diamond is small enough.
