Representation of Gaussian Isotropic Spin Random Fields

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 spin Gaussian isotropic field can be obtained with this construction. Our construction extends P. Lévy's original idea for the spherical Brownian Motion.

27 pages. Accepted for publication on Stoch. Processes Appl

References in corpus (2)

• Fourier coefficients of invariant random fields on homogeneous spaces of compact groups
• On Lévy's Brownian motion indexed by the elements of compact groups

Cited by in corpus (3)

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• Isotropic random spin weighted functions on $S^2$ vs isotropic random fields on $S^3$
• Expected Lipschitz-Killing curvatures for spin random fields and other non-isotropic fields