  We investigate the optimal configurations of n points on the unit sphere for
a class of potential functions. In particular, we characterize these optimal
configurations in terms of their approximation properties within frame theory.
Furthermore, we consider similar optimal configurations in terms of random
distributions of points on the sphere. In this probabilistic setting, we
characterize these optimal distributions by means of special classes of
probabilistic frames. Our work also indicates some connections between
statistical shape analysis and frame theory.
