Representations of SO(3) and angular polyspectra

Domenico Marinucci; Giovanni Peccati

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arXiv · 0807.0687

Representations of SO(3) and angular polyspectra

Domenico Marinucci·Giovanni Peccati

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Abstract

We characterize the angular polyspectra, of arbitrary order, associated with isotropic fields defined on the sphere S^2. 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.

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Domenico Marinucci, Giovanni Peccati. 2008-07-04. Representations of SO(3) and angular polyspectra. https://arxiv.org/abs/0807.0687

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