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On the characterization of isotropic Gaussian fields on homogeneous spaces of compact groups. (English) Zbl 1128.60039
Summary: Let \(T\) be a random field weakly invariant under the action of a compact group \(G\). We give conditions ensuring that the independence of the random Fourier coefficients is equivalent to Gaussianity. As a consequence, in general it is not possible to simulate a non-Gaussian invariant random field through its Fourier expansion using independent coefficients.

60G60 Random fields
60B15 Probability measures on groups or semigroups, Fourier transforms, factorization
60E05 Probability distributions: general theory
43A30 Fourier and Fourier-Stieltjes transforms on nonabelian groups and on semigroups, etc.
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