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

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

2007-04-12

arxiv.org/abs/0704.1575v1

Mathematics

Probability

Scientific paper

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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