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

Let be a random field indexed by an Abelian compact group G, and suppose that has the form , where T is Gaussian and stationary. The aim of this paper is to establish high-frequency central limit theorems for the Fourier coefficients associated with . The proofs of our main results involve recently established criteria for the weak convergence of multiple Wiener-Itô integrals. Our research is motivated by physical applications, mainly related to the probabilistic modelling of the cosmic microwave background radiation. In this connection, the case of the n-dimensional torus is analyzed in detail.