Representations of SO(3) and angular polyspectra

Domenico Marinucci (1) , Giovanni Peccati (2)

1 DIPMAT - Dipartimento di Matematica [Roma II]
2 LSTA - Laboratoire de Statistique Théorique et Appliquée

We characterize the angular polyspectra, of arbitrary order, associated with isotropic fields defined on the sphere S². 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.

Mots clés: Group Representations; Isotropy; Polyspectra; Spherical Random Fields

Domaines: Probabilités [math.PR]; Théorie des groupes [math.GR]

Domenico Marinucci, Giovanni Peccati. Representations of SO(3) and angular polyspectra. 2008. ⟨hal-00293251⟩