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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.

##### MSC:
 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.
##### Keywords:
isotropic random field; Fourier expansion
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