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A central limit theorem and higher order results for the angular bispectrum
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  • Published: 17 July 2007

A central limit theorem and higher order results for the angular bispectrum

  • Domenico Marinucci1 

Probability Theory and Related Fields volume 141, pages 389–409 (2008)Cite this article

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Abstract

The angular bispectrum of spherical random fields has recently gained an enormous importance, especially in connection with statistical inference on cosmological data. In this paper, we analyze its moments and cumulants of arbitrary order and we use these results to establish a multivariate central limit theorem and higher order approximations. The results rely upon combinatorial methods from graph theory and a detailed investigation for the asymptotic behavior of coefficients arising in matrix representation theory for the group of rotations SO(3).

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Rome “Tor Vergata”, Via della Ricerca Scientifica 1, 00133, Rome, Italy

    Domenico Marinucci

Authors
  1. Domenico Marinucci
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Corresponding author

Correspondence to Domenico Marinucci.

Additional information

I am very grateful to an associate editor and two referees for many useful comments, and to M. W. Baldoni and P. Baldi for discussions on an earlier version.

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Cite this article

Marinucci, D. A central limit theorem and higher order results for the angular bispectrum. Probab. Theory Relat. Fields 141, 389–409 (2008). https://doi.org/10.1007/s00440-007-0088-8

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  • Received: 15 July 2005

  • Revised: 16 May 2007

  • Published: 17 July 2007

  • Issue Date: July 2008

  • DOI: https://doi.org/10.1007/s00440-007-0088-8

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Keywords

  • Spherical random fields
  • Angular bispectrum
  • Central limit theorem
  • Higher order approximations

Mathematics Subject Classification (2000)

  • Primary: 60G60
  • Secondary: 60F05
  • 62M15
  • 62M40
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