Beyond the Lognormal Approximation: a General Simulation Scheme
  We present a public code to generate random fields with an arbitrary
probability distribution function (PDF) and an arbitrary correlation function.
The algorithm is cosmology-independent, applicable to any stationary stochastic
process over a three dimensional grid. We implement it in the case of the
matter density field, showing its benefits over the lognormal approximation,
which is often used in cosmology for generation of mock catalogues. We find
that the covariance of the power spectrum from the new fast realizations is
more accurate than that from a lognormal model. As a proof of concept, we also
apply the new simulation scheme to the divergence of the Lagrangian
displacement field. We find that information from the correlation function and
the PDF of the displacement-divergence provides modest improvement over other
standard analytical techniques to describe the particle field in the
simulation. This suggests that further progress in this direction should come
from multi-scale or non-local properties of the initial matter distribution.
