The needlets bispectrum

The purpose of this paper is to join two different threads of the recent literature on random fields on the sphere, namely the statisti- cal analysis of higher order angular power spectra on one hand, and the construction of second-generation wavelets on the sphere on the other. To this aim, we introduce the needlets bispectrum and we derive a number of convergence results. Here, the limit theory is developed in the high resolu- tion sense. The leading motivation of these results is the need for statistical procedures for searching non-Gaussianity in Cosmic Microwave Background radiation. AMS 2000 subject classifications: Primary 62G20; secondary 62M15, 60B15, 60G60. Keywords and phrases: Bispectrum, Needlets, Spherical Random Fields, Cosmic Microwave Background Radiation, High Resolution Asymptotics.

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