Bernoulli

  • Bernoulli
  • Volume 16, Number 3 (2010), 798-824.

Group representations and high-resolution central limit theorems for subordinated spherical random fields

Domenico Marinucci and Giovanni Peccati

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Abstract

We study the weak convergence (in the high-frequency limit) of the frequency components associated with Gaussian-subordinated, spherical and isotropic random fields. In particular, we provide conditions for asymptotic Gaussianity and establish a new connection with random walks on the hypergroup $\widehat{\mathit{SO}(3)}$ (the dual of the group of rotations $SO(3)$), which mirrors analogous results previously established for fields defined on Abelian groups (see Marinucci and Peccati [Stochastic Process. Appl. 118 (2008) 585–613]). Our work is motivated by applications to cosmological data analysis.

Article information

Source
Bernoulli, Volume 16, Number 3 (2010), 798-824.

Dates
First available in Project Euclid: 6 August 2010

Permanent link to this document
https://projecteuclid.org/euclid.bj/1281099885

Digital Object Identifier
doi:10.3150/09-BEJ230

Mathematical Reviews number (MathSciNet)
MR2730649

Zentralblatt MATH identifier
1284.60099

Keywords
Clebsch–Gordan coefficients cosmic microwave background Gaussian subordination group representations high resolution asymptotics spectral representation spherical random fields

Citation

Marinucci, Domenico; Peccati, Giovanni. Group representations and high-resolution central limit theorems for subordinated spherical random fields. Bernoulli 16 (2010), no. 3, 798--824. doi:10.3150/09-BEJ230. https://projecteuclid.org/euclid.bj/1281099885


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