Representation of Gaussian isotropic spin random fields

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Abstract

We develop a technique for the construction of random fields on algebraic structures. We deal with two general situations: random fields on homogeneous spaces of a compact group and in the spin line bundles of the 2-sphere. In particular, every complex Gaussian isotropic spin random field can be represented in this way. Our construction extends P. Lévy’s original idea for the spherical Brownian motion.

MSC

60G60
33C55
57T30

Keywords

Gaussian random fields
Spherical harmonics
Line bundles
Induced representations

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