Brazilian Journal of Probability and Statistics

Angular spectra for non-Gaussian isotropic fields

György Terdik

Full-text: Open access

Abstract

Cosmic microwave background (CMB) Anisotropies is a subject of intensive research in recent years, and therefore it is necessary to develop suitable theory and methods for the analysis of isotropic fields on spheres. The main object of our paper is to show that the polyspectra can be given as the coefficients of the orthogonal expansion of cumulants of the field in terms of irreducible tensor products of spherical harmonics. We obtain necessary and sufficient conditions for isotropy of a non-Gaussian field and the conditions are stated in terms of higher order spectra (polyspectra). The relation between cumulants and spectra gives a new method of estimating spectra.

Article information

Source
Braz. J. Probab. Stat., Volume 29, Number 4 (2015), 833-865.

Dates
Received: December 2013
Accepted: May 2014
First available in Project Euclid: 17 September 2015

Permanent link to this document
https://projecteuclid.org/euclid.bjps/1442513449

Digital Object Identifier
doi:10.1214/14-BJPS249

Mathematical Reviews number (MathSciNet)
MR3397396

Zentralblatt MATH identifier
1328.83219

Keywords
Bispectrum trispectrum angular polyspectra CMB non-Gaussianity spherical random fields isotropy

Citation

Terdik, György. Angular spectra for non-Gaussian isotropic fields. Braz. J. Probab. Stat. 29 (2015), no. 4, 833--865. doi:10.1214/14-BJPS249. https://projecteuclid.org/euclid.bjps/1442513449


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