On the Limiting Behaviour of Needlets Polyspectra

Дата и время публикации : 2013-07-17T16:36:34Z

Авторы публикации и институты :
Valentina Cammarota
Domenico Marinucci

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Первичная категория: math.PR

Все категории : math.PR, astro-ph.CO, 60G60, 62M15, 42C15

Краткий обзор статьи: This paper provides quantitative Central Limit Theorems for nonlinear transforms of spherical random fields, in the high frequency limit. The sequences of fields that we consider are represented as smoothed averages of spherical Gaussian eigenfunctions and can be viewed as random coefficients from continuous wavelets/needlets; as such, they are of immediate interest for spherical data analysis. In particular, we focus on so-called needlets polyspectra, which are popular tools for nonGaussianity analysis in the astrophysical community, and on the area of excursion sets. Our results are based on Stein-Maliavin approximations for nonlinear transforms of Gaussian fields, and on an explicit derivation on the high-frequency limit of their variances, which may have some independent interest.

Category: Physics