Baldi, Paolo; Marinucci, Domenico; Varadarajan, Veeravalli S. On the characterization of isotropic Gaussian fields on homogeneous spaces of compact groups. (English) Zbl 1128.60039 Electron. Commun. Probab. 12, 291-302 (2007). 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. Cited in 1 ReviewCited in 14 Documents 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 PDFBibTeX XMLCite \textit{P. Baldi} et al., Electron. Commun. Probab. 12, 291--302 (2007; Zbl 1128.60039) Full Text: DOI arXiv EuDML