Ergodicity and Gaussianity for Spherical Random Fields

Abstract

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.

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

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• The defect variance of random spherical harmonics
• On the Excursion Sets of Spherical Gaussian Eigenfunctions
• Coordinate changed random fields on manifolds
• Gaussian semiparametric estimates on the unit sphere
• Exchangeable pairs on Wiener chaos
• Coordinates changed random fields on the sphere
• Aliasing effects for random fields over spheres of arbitrary dimension
• Models of space-time random fields on the sphere