Representations of SO(3) and angular polyspectra

D. Marinucci and G. Peccati

Journal of Multivariate Analysis, 2010, vol. 101, issue 1, 77-100

Abstract: We characterize the angular polyspectra, of arbitrary order, associated with isotropic fields defined on the sphere S2={(x,y,z):x2+y2+z2=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.

Keywords: Group; representations; Isotropy; Polyspectra; Spherical; random; fields (search for similar items in EconPapers)
Date: 2010
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Citations: View citations in EconPapers (1)

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