Pfaffian Schur 过程与半象限中的最后通过渗流
Pfaffian Schur processes and last passage percolation in a half-quadrant
AI总结：
该研究在Pfaffian Schur过程框架下分析半象限最后通过渗流模型，证明不同区域涨落的分布规律，得到二维交叉行为并提出处理发散相关核的方法，推测交叉行为在半空间KPZ生长模型中普遍存在。
摘要：
我们在Pfaffian Schur过程的框架下，对半象限中的最后通过渗流展开研究。针对带指数权重的模型，我们证明：到达对角线上某点的最后通过时间的涨落，依对角线沿线权重的大小不同，分别服从GSE Tracy-Widom分布、GOE Tracy-Widom分布或高斯分布；在远离对角线的区域，通过时间的涨落则服从GUE Tracy-Widom分布。当对角线权重的大小同时缩放至临界点附近时，我们通过研究靠近对角线处最后通过时间的多点分布，得到了GUE、GOE与GSE分布之间的二维交叉行为。我们推测这种交叉行为在半空间的KPZ生长模型中普遍存在。研究过程中，我们提出了一种方法，用于处理标度极限下点发生碰撞的点过程的发散相关核。
英文摘要：
We study last passage percolation in a half-quadrant, which we analyze within the framework of Pfaffian Schur processes. For the model with exponential weights, we prove that the fluctuations of the last passage time to a point on the diagonal are either GSE Tracy-Widom distributed, GOE Tracy-Widom distributed, or Gaussian, depending on the size of weights along the diagonal. Away from the diagonal, the fluctuations of passage times follow the GUE Tracy-Widom distribution. We also obtain a two-dimensional crossover between the GUE, GOE and GSE distribution by studying the multipoint distribution of last passage times close to the diagonal when the size of the diagonal weights is simultaneously scaled close to the critical point. We expect that this crossover arises universally in KPZ growth models in half-space. Along the way, we introduce a method to deal with diverging correlation kernels of point processes where points collide in the scaling limit.
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