Correlations between Maxwell's multipoles for Gaussian random functions on the sphere

Maxwell's multipoles are a natural geometric characterization of real functions on the sphere (with fixed ⌊). The correlations between multipoles for Gaussian random functions are calculated by mapping the spherical functions to random polynomials. In the limit of high ⌊, the 2-point function tends to a form previously derived by Hannay in the analogous problem for the Majorana sphere. The application to the cosmic microwave background (CMB) is discussed