论文标题
关于平面随机波的节点长度的减少原理的注释
A Note on the Reduction Principle for the Nodal Length of Planar Random Waves
论文作者
论文摘要
受到最新工作的启发[MRW20]，我们证明了平面随机波$ b_ {e} $的节点长度，即其零套件的长度$ b_ {e}^{ - 1}（0）$，在$ l^{2} $ limit in $ limitional in highty上是同等的，在$ l^{2} $ limit中， $ h_ {4}（b_ {e}（x））$，$ h_4 $是第四个赫米特多项式。作为直接的结果，我们获得了瓦斯汀距离的中心极限定理。这补充了[NPR19]和[PV20]中的最新发现。
Inspired by the recent work [MRW20], we prove that the nodal length of a planar random wave $B_{E}$, i.e. the length of its zero set $B_{E}^{-1}(0)$, is asymptotically equivalent, in the $L^{2}$-sense and in the high-frequency limit $E\rightarrow \infty$, to the integral of $H_{4}(B_{E}(x))$, $H_4$ being the fourth Hermite polynomial. As a straightforward consequence, we obtain a central limit theorem in Wasserstein distance. This complements recent findings in [NPR19] and [PV20].
