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Theory of Probability and Mathematical Statistics

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Spectral expansions of random sections of homogeneous vector bundles

Author: A. Malyarenko
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 97 (2017).
Journal: Theor. Probability and Math. Statist. 97 (2018), 151-165
MSC (2010): Primary 60G60; Secondary 83F05
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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Additional Information

A. Malyarenko
Affiliation: Division of Applied Mathematics, School of Education, Culture and Communication, Mälardalen University, Box 883, SE-721 23 Västerås, Sweden

Keywords: Random field, vector bundle, cosmology
Received by editor(s): August 4, 2017
Published electronically: February 21, 2019
Additional Notes: This paper was written with the financial support of the Data Innovation Research Institute, Cardiff University, United Kingdom
Dedicated: Dedicated to my teacher Mykhailo Yadrenko in the occasion of his 85th birthday
Article copyright: © Copyright 2019 American Mathematical Society