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Using fits to numerical simulations, we show that the entire hierarchy ofmoments quickly ceases to provide a complete description of the convergenceone-point probability density function leaving the linear regime. This suggeststhat the full N-point correlation function hierarchy of the convergence fieldbecomes quickly generically incomplete and a very poor cosmological probe onnonlinear scales. At the scale of unit variance, only 5% of the Fisherinformation content of the one-point probability density function is stillcontained in its hierarchy of moments, making clear that information escapingthe hierarchy is a far stronger effect than information propagating to higherorder moments. It follows that the constraints on cosmological parametersachievable through extraction of the entire hierarchy become suboptimal bylarge amounts. A simple logarithmic mapping makes the moment hierarchy wellsuited again for parameter extraction.

Information escaping the correlation hierarchy of the convergence field in the study of cosmological parameters