A note on 3d-monochromatic random waves and cancellation

IF 0.6 4区 数学 Q4 STATISTICS & PROBABILITY
F. Dalmao
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引用次数: 1

Abstract

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.
关于三维单色随机波及其消除的一点注记
在本文中,我们证明了在$\R^3$中,限制于递增域的复值单色随机波的节点长度的渐近方差在域的体积中是线性的。结合前面的结果,这表明一个中心极限定理适用于$3$维的单色随机波。我们将实值$2$维单色随机波的节点长度的方差进行了比较,其中观察到更快的发散率,这一事实与Berry的抵消现象有关。此外,我们还证明了集中现象的发生。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
CiteScore
1.10
自引率
0.00%
发文量
48
期刊介绍: ALEA publishes research articles in probability theory, stochastic processes, mathematical statistics, and their applications. It publishes also review articles of subjects which developed considerably in recent years. All articles submitted go through a rigorous refereeing process by peers and are published immediately after accepted. ALEA is an electronic journal of the Latin-american probability and statistical community which provides open access to all of its content and uses only free programs. Authors are allowed to deposit their published article into their institutional repository, freely and with no embargo, as long as they acknowledge the source of the paper. ALEA is affiliated with the Institute of Mathematical Statistics.
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