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