论文标题
随机分区中的通用边缘缩放
Universal edge scaling in random partitions
论文作者
论文摘要
我们建立了随机分区的通用边缘缩放极限，其无限参数分布称为Schur度量。我们基于schr {Ö} dinger-type微分方程，探索波函数的渐近行为，该波动函数是相应内核的构建块。我们表明，波函数通常是渐近函数及其高阶类似物的边缘缩放限制。我们构建了来自Scalins限制的波函数的相应高阶通风内核和Tracy-Widom分布，并讨论了其与大尺寸矩阵模型中多政治相变的含义。我们还通过对波函数的半古典分析讨论随机分区的极限形状。
We establish the universal edge scaling limit of random partitions with the infinite-parameter distribution called the Schur measure. We explore the asymptotic behavior of the wave function, which is a building block of the corresponding kernel, based on the Schr{ö}dinger-type differential equation. We show that the wave function is in general asymptotic to the Airy function and its higher-order analogs in the edge scaling limit. We construct the corresponding higher-order Airy kernel and the Tracy-Widom distribution from the wave function in the scalins limit, and discuss its implication to the multicritical phase transition in the large size matrix model. We also discuss the limit shape of random partitions through the semi-classical analysis of the wave function.
