论文标题
$ 3D $ - 单色随机波和取消的注释
A note on $3d$-monochromatic random waves and cancellation
论文作者
论文摘要
在本说明中，我们证明，限制在$ \ r^3 $中限制在域中增加域的复合物值单色随机波的渐近方差在域的体积中是线性的。结合以前的结果，这表明中央限制定理以$ 3 $维的单色随机波的成立为原样。我们将实际价值$ 2 $维的单色随机波的淋巴结长度的方差进行比较，观察到更快的发散率，这一事实与浆果的取消现象有关。此外，我们表明发生了一种集中现象。
In this note we prove that the asymptotic variance of the nodal length of complex-valued monochromatic random waves restricted to an increasing domain in $\R^3$ is linear in the volume of the domain. Put together with previous results this shows that a Central Limit Theorem holds true for $3$-dimensional monochromatic random waves. We compare with the variance of the nodal length of the real-valued $2$-dimensional monochromatic random waves where a faster divergence rate is observed, this fact is connected with Berry's cancellation phenomenon. Moreover, we show that a concentration phenomenon takes place.
