论文标题
Baik-Rains分布的PDE系统
A System of PDEs for the Baik-Rains Distribution
论文作者
论文摘要
已经发现，kadomtsev-petviashvili（KP）方程控制了许多随机增长模型波动的分布，尤其是Tracy-Widom分布似乎是KP方程的特殊自相似溶液。我们证明，Baik-Rains分布的抗衍生作用，该分布控制着KPZ通用类中模型的波动，从固定初始数据开始，可以满足KP方程。我们从满足KP的KPZ方程的生成函数的确定公式开始。然后，我们观察到该方程仍处于较大的时间限制。
It has been discovered that the Kadomtsev-Petviashvili(KP) equation governs the distribution of the fluctuation of many random growth models, in particular, the Tracy-Widom distributions appear as special self-similar solutions of the KP equation. We prove that the anti-derivative of Baik-Rains distribution, which governs the fluctuation of the models in the KPZ universality class starting with stationary initial data, satisfies the KP equation. We start from a determinantal formula of the generating function of the KPZ equation, which satisfies the KP. Then we observe that the equation still holds in the large time limit.
