论文标题
KPZ和定期KPZ固定点的微分方程
Differential equations for the KPZ and periodic KPZ fixed points
论文作者
论文摘要
KPZ固定点是一个2D随机场，猜想是KPZ通用类中模型高度功能的通用限制波动场。同样，周期性的KPZ固定点是空间周期性模型的猜想通用场。对于这两个字段，最近都计算了它们在时空域中的多点分布。我们表明，对于狭窄的wedge初始条件，这些多点分布可以用所谓的集成运算符表示。然后，我们考虑包括由KPZ和周期性KPZ固定点产生的操作员的类别，并发现它们与各种矩阵积分的微分方程（例如耦合矩阵MKDV方程）有关，耦合矩阵NLS方程与复杂的时间和矩阵KP-IIIIIE方程相关。当应用于KPZ固定点时，我们的结果扩展了以前已知的微分方程，以对单点分布和等级的多位分布扩展到多时间，多位置设置。
The KPZ fixed point is a 2d random field, conjectured to be the universal limiting fluctuation field for the height function of models in the KPZ universality class. Similarly, the periodic KPZ fixed point is a conjectured universal field for spatially periodic models. For both fields, their multi-point distributions in the space-time domain have been computed recently. We show that for the case of the narrow-wedge initial condition, these multi-point distributions can be expressed in terms of so-called integrable operators. We then consider a class of operators that include the ones arising from the KPZ and the periodic KPZ fixed points, and find that they are related to various matrix integrable differential equations such as coupled matrix mKdV equations, coupled matrix NLS equations with complex time, and matrix KP-II equations. When applied to the KPZ fixed points, our results extend previously known differential equations for one-point distributions and equal-time, multi-position distributions to multi-time, multi-position setup.
