论文标题
满足随机波模型的单色波的结节集
Nodal set of monochromatic waves satisfying the Random Wave Model
论文作者
论文摘要
我们在$ \ mathbb {r}^m $中构建针对Helmholtz方程的确定性解决方案，这些解决方案对随机波模型进行了相应的影响。然后，我们找到了它们的淋巴结域的数量，它们的淋巴结音量以及淋巴结的拓扑和嵌套树木，它们在起源周围成长的球中。所考虑的函数的伪随机行为的证明是对脱离随机化技术的铰链，并通过计算其$ l^p $ norms来进行。对淋巴结集的研究取决于其稳定性和对其双倍指数的评估。
We construct deterministic solutions to the Helmholtz equation in $\mathbb{R}^m$ which behave accordingly to the Random Wave Model. We then find the number of their nodal domains, their nodal volume and the topologies and nesting trees of their nodal set in growing balls around the origin. The proof of the pseudo-random behaviour of the functions under consideration hinges on a de-randomisation technique pioneered by Bourgain and proceeds via computing their $L^p$-norms. The study of their nodal set relies on its stability properties and on the evaluation of their doubling index, in an average sense.
