Ergodicity and Gaussianity for spherical random fields. (English) Zbl 1310.37022
Summary: 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 radiation data analysis.{
©2010 American Institute of Physics}
©2010 American Institute of Physics}
MSC:
| 37H10 | Generation, random and stochastic difference and differential equations |
| 60G15 | Gaussian processes |
| 83F05 | Relativistic cosmology |
| 85A25 | Radiative transfer in astronomy and astrophysics |
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