A Central Limit Theorem and Higher Order Results for the Angular Bispectrum

Details A Central Limit Theorem and Higher Order Results for the Angular Bispectrum A Central Limit Theorem and Higher Order Results for the Angular Bispectrum

2005-09-19

arxiv.org/abs/math/0509430v1

Probability Theory and Related Fields, 141, pp. 389-409 (2008)

Mathematics

Probability

Submitted for publication

Scientific paper

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 provide expressions for its moments 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 behaviour of Clebsch-Gordan coefficients; the latter are widely used in representation theory and quantum theory of angular momentum.

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