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

Let (T) over tilde (g) be a random field indexed by an Abelian compact group G, and suppose that (T) over tilde has the form (T) over tilde (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-Ito 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. (C) 2007 Elsevier B.V. All rights reserved.