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

Let T ˜ ( g ) be a random field indexed by an Abelian compact group G , and suppose that T ˜ has the form T ˜ ( g ) = F ( T ( g ) ) , 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 T ˜ . 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.