The defect variance of random spherical harmonics
The defect variance of random spherical harmonics
复制标题
DOI：
10.1088/1751-8113/44/35/355206
复制
发表时间：
2011-03
期刊：
影响因子：
--
通讯作者：
D. Marinucci;I. Wigman
中科院分区：
文献类型：
--
作者：
D. Marinucci;I. Wigman
函数的缺陷被定义为正区域和负区域的度量之间的差。本文开始分析随机高斯球谐函数的缺陷分布。通过一个简单的论点，缺陷是非平凡的，只有偶数次和期望值总是为零。我们的主要结果是评估的缺陷方差，渐近的高频限制。与随机本征函数的其他几何泛函一样，该缺陷可以作为一种工具来探测球形随机场的统计性质，这是现代宇宙学数据分析的一个非常感兴趣的话题。
The defect of a function is defined as the difference between the measure of the positive and negative regions. In this paper, we begin the analysis of the distribution of defect of random Gaussian spherical harmonics. By an easy argument, the defect is non-trivial only for even degree and the expected value always vanishes. Our principal result is evaluating the defect variance, asymptotically in the high-frequency limit. As other geometric functionals of random eigenfunctions, the defect may be used as a tool to probe the statistical properties of spherical random fields, a topic of great interest for modern cosmological data analysis.