论文标题
在3道和一般取消现象上的节点集的波动
Fluctuations of nodal sets on the 3-torus and general cancellation phenomena
论文作者
论文摘要
2017年，Benatar和Maffucci Arxiv：1708.07015建立了一种渐近法，以在高能限制下3道路上的算术随机波的鼻表面方差。在随后的工作中，cammarota arxiv：1708.07679证明了淋巴结表面的通用非高斯极限定理。在本文中，我们研究了淋巴结的长度和与两个和三个独立的算术算术随机波相关的淋巴结相交点的数量，在3托里上具有相同的频率。对于这些数量，我们计算其期望值，渐近方差及其限制分布。我们的结果基于Wiener-Itô扩展，并自然地补充了Cammarota Arxiv的发现：1708.07679。我们分析的核心是一种抽象的取消现象，适用于我们认为具有独立兴趣的任意高斯随机领域的水平集。
In 2017, Benatar and Maffucci arXiv:1708.07015 established an asymptotic law for the variance of the nodal surface of arithmetic random waves on the 3-torus in the high-energy limit. In a subsequent work, Cammarota arXiv:1708.07679 proved a universal non-Gaussian limit theorem for the nodal surface. In this paper, we study the nodal intersection length and the number of nodal intersection points associated, respectively, with two and three independent arithmetic random waves of same frequency on the 3-torus. For these quantities, we compute their expected value, asymptotic variance as well as their limiting distribution. Our results are based on Wiener-Itô expansions for the volume and naturally complement the findings of Cammarota arXiv:1708.07679. At the core of our analysis lies an abstract cancellation phenomenon applicable to the study of level sets of arbitrary Gaussian random fields, that we believe has independent interest.
