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.
Publié le : 2010-08-15
Classification:
Clebsch–Gordan coefficients,
cosmic microwave background,
Gaussian subordination,
group representations,
high resolution asymptotics,
spectral representation,
spherical random fields
@article{1281099885,
author = {Marinucci, Domenico and Peccati, Giovanni},
title = {Group representations and high-resolution central limit theorems for subordinated spherical random fields},
journal = {Bernoulli},
volume = {16},
number = {1},
year = {2010},
pages = { 798-824},
language = {en},
url = {http://dml.mathdoc.fr/item/1281099885}
}
Marinucci, Domenico; Peccati, Giovanni. Group representations and high-resolution central limit theorems for subordinated spherical random fields. Bernoulli, Tome 16 (2010) no. 1, pp. 798-824. http://gdmltest.u-ga.fr/item/1281099885/