High-frequency asymptotics for subordinated isotropic fields on an Abelian compact group

Let T* be a random field indexed by an Abelian compact group G, and suppose that T* has the form T* = F(T(g)), where T is Gaussian and isotropic. The aim of this paper is to establish high-frequency central limit theorems for the Fourier coefficients associated to T*. The proofs of our main results involve recently established criteria for the weak convergence of multiple Wiener-It\^{o} integrals. Our research is motivated by physical applications, mainly related to the probabilistic modelization of the Cosmic Microwave Background radiation. In this connection, the case of the n-dimensional torus is analyzed in detail.