Group representations and high-resolution central limit theorems for subordinated spherical random fields

We study the weak convergence (in the high-frequency limit) of the frequency components associated with Gaussian-subordinated, spherical and isotropic random fields. In particular, we provide conditions for asymptotic Gaussianity and establish a new connection with random walks on the hypergroup 50(3) (the dual of the group of rotations 50(3)), which mirrors analogous results previously established for fields defined on Abelian groups (see Marinucci and Peccati [Stochastic Process. Appl. 118 (2008) 585-613]). Our work is motivated by applications to cosmological data analysis.