论文标题
按零件和KPZ两点功能进行集成
Integration by Parts and the KPZ Two-Point Function
论文作者
论文摘要
在本文中，我们考虑了KPZ固定点从具有任意扩散系数的双面布朗运动开始。我们应用了Malliavin微积分的零件公式的集成，以建立空间衍生过程的两点（协方差）函数与通风过程的最大值的位置以及Brownian Motion减去抛物线的关键关系。按零件进行集成还使我们可以根据KPZ固定点方差的第二个导数来推断此位置的密度。在固定方案中，我们发现与限制二等粒子波动相同的密度相同。我们进一步开发了Stein方法的适应，这意味着从初始数据中的空间衍生过程渐近独立性。
In this article we consider the KPZ fixed point starting from a two-sided Brownian motion with an arbitrary diffusion coefficient. We apply the integration by parts formula from Malliavin calculus to establish a key relation between the two-point (covariance) function of the spatial derivative process and the location of the maximum of an Airy process plus Brownian motion minus a parabola. Integration by parts also allows us to deduce the density of this location in terms of the second derivative of the variance of the KPZ fixed point. In the stationary regime, we find the same density related to limit fluctuations of a second-class particle. We further develop an adaptation of Stein's method that implies asymptotic independence of the spatial derivative process from the initial data.
