论文标题
算术随机波的Lipschitz杀死曲率
Lipschitz-Killing Curvatures for Arithmetic Random Waves
论文作者
论文摘要
在本文中，我们表明，算术随机波（Toral Gaussian征收特征）的游览集的Lipschitz杀死曲率在高频方向上是由单个混乱的组成部分主导的。后者可以写入阈值参数的简单显式函数乘以这些随机字段的居中规范。结果，这些几何函数在高能极限中完全相关。派生的公式显示出与圆形单位球体上相关结果的明确类比，并提出了在riemannian歧管上随机特征函数的几何功能的一般公式。
In this paper, we show that the Lipschitz-Killing Curvatures for the excursion sets of Arithmetic Random Waves (toral Gaussian eigenfunctions) are dominated, in the high-frequency regime, by a single chaotic component. The latter can be written as a simple explicit function of the threshold parameter times the centered norm of these random fields; as a consequence, these geometric functionals are fully correlated in the high-energy limit. The derived formulae show a clear analogy with related results on the round unit sphere and suggest the existence of a general formula for geometric functionals of random eigenfunctions on Riemannian manifolds.
