Fourier coefficients of invariant random fields on homogeneous spaces of compact groups

2013/04/18 by Paolo Baldi, Baldi, Paolo, Stefano Trapani +1
Mathematics · #43A30 #FOS: Mathematics #Geometry and complex manifolds #Mathematical Analysis and Transform Methods #Primary 60B15 #Probability (math.PR) #Secondary 60E05 #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.1304.5142

openalex publication_date 2013/04/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let T be a random field invariant under the action of a compact group G. In the line of previous work we investigate properties of the Fourier coefficients as orthogonality and Gaussianity. In particular we give conditions ensuring that independence of the random Fourier coefficients implies 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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