Information escaping the correlation hierarchy of the convergence field
  in the study of cosmological parameters
  Using fits to numerical simulations, we show that the entire hierarchy of
moments quickly ceases to provide a complete description of the convergence
one-point probability density function leaving the linear regime. This suggests
that the full N-point correlation function hierarchy of the convergence field
becomes quickly generically incomplete and a very poor cosmological probe on
nonlinear scales. At the scale of unit variance, only 5% of the Fisher
information content of the one-point probability density function is still
contained in its hierarchy of moments, making clear that information escaping
the hierarchy is a far stronger effect than information propagating to higher
order moments. It follows that the constraints on cosmological parameters
achievable through extraction of the entire hierarchy become suboptimal by
large amounts. A simple logarithmic mapping makes the moment hierarchy well
suited again for parameter extraction.
