论文标题
KPZ类中的可解决模型：通过定期和自由边界措施的方法
Solvable models in the KPZ class: approach through periodic and free boundary Schur measures
论文作者
论文摘要
我们探讨了作者在最近的论文[arxiv：2106.11922]中建立的$ q $ whittaker措施与周期性和自由边界措施之间对应关系的概率后果。结果是在KPZ类中的随机模型的综合理论，其中确切的公式从映射到明确的确定性和PFAFFIAN点过程。我们发现已知结果的新变体是ASEP在生产线上当前分布的确定性公式，以及新的结果，例如Fredholm Pfaffian公式，用于在半空间中分布Log Gamma聚合物模型的点对点分区函数。在后一种情况下，缩放限制和渐近分析允许建立Baik-Rains相变，以在原点的半线上KPZ方程的高度函数。
We explore probabilistic consequences of correspondences between $q$-Whittaker measures and periodic and free boundary Schur measures established by the authors in the recent paper [arXiv:2106.11922]. The result is a comprehensive theory of solvability of stochastic models in the KPZ class where exact formulas descend from mapping to explicit determinantal and pfaffian point processes. We discover new variants of known results as determinantal formulas for the current distribution of the ASEP on the line and new results such as Fredholm pfaffian formulas for the distribution of the point-to-point partition function of the Log Gamma polymer model in half space. In the latter case, scaling limits and asymptotic analysis allow to establish Baik-Rains phase transition for height function of the KPZ equation on the half line at the origin.
