Some central limit results on stochastic processes in a compact connected 2-point homogeneous space $E(d)$ of growing dimension $d$ are reformulated within the theory of polynomial convolution structures. This approach stresses the algebraic-topological relationship between those structures and the asymptotic properties of the stochastic processes under consideration, in particular of random walks and Gaussian processes on $E(d)$ with $d\to\infty$.