A lower bound for the Bogomolny–Schmit constant for random monochromatic plane waves
A lower bound for the Bogomolny–Schmit constant for random monochromatic plane waves
复制标题
随机单色平面波的博戈莫尔尼-施密特常数的下界
DOI：
10.4310/mrl.2019.v26.n4.a9
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发表时间：
2018
影响因子：
1
通讯作者：
A. Rivera
中科院分区：
文献类型：
--
作者：
M. Ingremeau;A. Rivera
本文讨论了随机单色平面波的节点域。Nazarov和Sodin证明了半径为$R$的圆盘中包含的这种节点域的期望个数与大的$R$极限中的$\pi R^2$成正比。然而，从数学角度来看，人们对比例常数的值知之甚少。这个注解的目的是得到这个常数的值的一个下界，我的初等平均值。
This note deals with nodal domains of random monochromatic plane waves. It was shown by Nazarov and Sodin that the expected number of such nodal domains included in a disk of radius $R$ is proportional to $\pi R^2$ in the large $R$ limit. However, very little is known on the value of the proportionality constant from a mathematical point of view. The aim of this note is to obtain a lower bound on the value of this constant my elementary means.