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

P. Baldi; D. Marinucci; V. S. Varadarajan

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arXiv · 0704.1575

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

P. Baldi·D. Marinucci·V. S. Varadarajan

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Abstract

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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P. Baldi, D. Marinucci, V. S. Varadarajan. 2007-04-12. On the characterization of isotropic Gaussian fields on homogeneous spaces of compact groups. https://arxiv.org/abs/0704.1575

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