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

Abstract

Maxwell's multipoles are a natural geometric characterisation of real functions on the sphere (with fixed $\ell$). The correlations between multipoles for gaussian random functions are calculated, by mapping the spherical functions to random polynomials. In the limit of high $\ell ,$ 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.

6 pages, 2 figures (revised version)

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