一个求解Baik-Rains分布的偏微分方程系统
A System of PDEs for the Baik-Rains Distribution
摘要：
Kadomtsev-Petviashvili（KP）方程控制着许多随机增长模型的涨落分布，特别是Tracy-Widom分布表现为KP方程的特殊自相似解。我们证明了Baik-Rains分布的反导数满足KP方程，该反导数决定了从平稳初始数据开始的KPZ普适类中模型的涨落。我们从满足KP的KPZ方程的母函数的行列式公式出发。然后我们观察到方程在大的时间极限下仍然成立。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
