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Invariant random fields in vector bundles and application to cosmology. (English. French summary) Zbl 1268.60072
The author provides various expansions of invariant random fields. Namely, the spectral decomposition of an invariant random field in a homogeneous vector bundle generated by an induced representation of a compact connected Lie group \(G\) is obtained. More details could be found in the recent book by the author [Invariant random fields on spaces with a group action. Berlin: Springer (2013; Zbl 1268.60006)]. The important case \(G=\mathrm{SO}(3)\) is considered as it is related with an analysis of the cosmic microwave background radiation. Various approaches to the study of relic radiation are compared. The role of the expansion coefficients, called electric multipoles and magnetic multipoles, is clarified.

60G60 Random fields
Zbl 1268.60006
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