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

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

2004-10-04

arxiv.org/abs/math-ph/0410004v2

J.Phys.A38:1653-1658,2005

Physics

Mathematical Physics

6 pages, 2 figures (revised version)

Scientific paper

10.1088/0305-4470/38/8/002

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.

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