发表机构
University of Science and Technology of China（中国科学技术大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文证明均匀交错符号矩阵的高度路径系在北极弧内点收敛于Airy线系，利用Pfaffian公式和重采样定律，结合Brownian Gibbs性质与强刻画定理。
AI 中文摘要
我们证明了均匀交错符号矩阵的高度水平路径系在西北北极弧的每个内点附近收敛到Airy线系。在标准双射下，这等价于冰点处域壁六顶点模型的密切路径的极限定理。证明有两个主要输入。可积输入是矩形冻结角概率的一个新的Pfaffian公式，由此我们得到顶部路径到GUE Tracy--Widom分布的单点收敛。概率输入是路径的严格有序中点编码的精确重采样定律及伴随的桥估计；这些为每个子序列极限提供了紧性和Brownian Gibbs性质。然后，Aggarwal和Huang的强刻画将每个这样的极限识别为Airy线系。
英文摘要
We prove that the height-level path ensemble of a uniform alternating sign matrix converges to the Airy line ensemble near every interior point of the north-west arctic arc. Under the standard bijection, this is equivalently a limit theorem for the osculating paths of the domain-wall six-vertex model at the ice point. The proof has two main inputs. The integrable input is a new Pfaffian formula for rectangular frozen-corner probabilities, from which we obtain one-point convergence of the top path to the GUE Tracy--Widom distribution. The probabilistic input is an exact resampling law and accompanying bridge estimates for a strictly ordered midpoint encoding of the paths; these yield tightness and the Brownian Gibbs property for every subsequential limit. Aggarwal and Huang's strong characterization then identifies each such limit as the Airy line ensemble.
Comments63 pages
