Ergodicity and Gaussianity for Spherical Random Fields

Details Ergodicity and Gaussianity for Spherical Random Fields Ergodicity and Gaussianity for Spherical Random Fields

2009-11-12

arxiv.org/abs/0911.2502v1

Mathematics

Probability

25 pages; PACS : 02.50-r, 98.70-Vc, 98.80-k

Scientific paper

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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