On the Limiting Behaviour of Needlets Polyspectra
  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.
