Spectral expansions of random sections of homogeneous vector bundles

Malyarenko, A.

doi:10.1090/tpms/1054

Spectral expansions of random sections of homogeneous vector bundles

Author: A. Malyarenko
Journal: Theor. Probability and Math. Statist. 97 (2018), 151-165
MSC (2010): Primary 60G60; Secondary 83F05
DOI: https://doi.org/10.1090/tpms/1054
Published electronically: February 21, 2019
MathSciNet review: 3746005
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Abstract: Tiny fluctuations of the Cosmic Microwave Background as well as various observable quantities obtained by spin raising and spin lowering of the effective gravitational lensing potential of distant galaxies and galaxy clusters are described mathematically as isotropic random sections of homogeneous spin and tensor bundles. We consider the three existing approaches to rigourous construction of the above objects, emphasising an approach based on the theory of induced group representations. Both orthogonal and unitary representations are treated in a unified manner. Several examples from astrophysics are included.

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