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Representations of SO(3) and angular polyspectra

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  • Marinucci, D.
  • Peccati, G.

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.

Suggested Citation

  • Marinucci, D. & Peccati, G., 2010. "Representations of SO(3) and angular polyspectra," Journal of Multivariate Analysis, Elsevier, vol. 101(1), pages 77-100, January.
    • Handle: RePEc:eee:jmvana:v:101:y:2010:i:1:p:77-100
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    References listed on IDEAS

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    1. Marinucci, Domenico & Peccati, Giovanni, 2008. "High-frequency asymptotics for subordinated stationary fields on an Abelian compact group," Stochastic Processes and their Applications, Elsevier, vol. 118(4), pages 585-613, April.
    2. Baldi, Paolo & Marinucci, Domenico, 2007. "Some characterizations of the spherical harmonics coefficients for isotropic random fields," Statistics & Probability Letters, Elsevier, vol. 77(5), pages 490-496, March.
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    Cited by:

    1. Jammalamadaka, S. Rao & Terdik, György H., 2019. "Harmonic analysis and distribution-free inference for spherical distributions," Journal of Multivariate Analysis, Elsevier, vol. 171(C), pages 436-451.

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