Enumerative combinatorics
Spatiospectral Concentration on a Sphere
SIAM Review
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We characterize the angular polyspectra, of arbitrary order, associated with isotropic fields defined on the sphere S^2={(x,y,z):x^2+y^2+z^2=1}. Our techniques rely heavily on group representation theory, and specifically on the properties of Wigner matrices and Clebsch-Gordan coefficients. The findings of the present paper constitute a basis upon which one can build formal procedures for the statistical analysis and the probabilistic modelization of the Cosmic Microwave Background radiation, which is currently a crucial topic of investigation in cosmology. We also outline an application to random data compression and ''simulation'' of Clebsch-Gordan coefficients.