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On the characterization of isotropic Gaussian fields on homogeneous spaces of compact groups

P.Baldi, D.Marinucci, V.S.Varadarajan
Arxiv ID: 0704.1575Last updated: 12/1/2021
Let T be a random field invariant under the action of a compact group G We give conditions ensuring that 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.

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