球面随机场的遍历性和高斯性
Ergodicity and Gaussianity for Spherical Random Fields
摘要：
研究了各向同性球面随机场在高分辨率（或高频）极限下的遍历性与渐近高斯性之间的关系。特别是，我们的研究结果表明，在各种各样的情况下，这两个条件是等价的，即样本角功率谱可以收敛到人口值，当且仅当基本场是渐近高斯，在高频意义上。这些发现可能有助于理解宇宙方差在宇宙微波背景辐射数据分析中的作用。
英文摘要：
We investigate the relationship between ergodicity and asymptotic Gaussianity of isotropic spherical random fields, in the high-resolution (or high-frequency) limit. In particular, our results suggest that under a wide variety of circumstances the two conditions are equivalent, i.e. the sample angular power spectrum may converge to the population value if and only if the underlying field is asymptotically Gaussian, in the high frequency sense. These findings may shed some light on the role of Cosmic Variance in Cosmic Microwave Background (CMB) radiation data analysis.
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