Testing the lognormality of the galaxy and weak lensing convergence
  distributions from Dark Energy Survey maps
  It is well known that the probability distribution function (PDF) of galaxy
density contrast is approximately lognormal; whether the PDF of mass
fluctuations derived from weak lensing convergence (kappa_WL) is lognormal is
less well established. We derive PDFs of the galaxy and projected matter
density distributions via the Counts in Cells (CiC) method. We use maps of
galaxies and weak lensing convergence produced from the Dark Energy Survey
(DES) Science Verification data over 139 deg^2. We test whether the underlying
density contrast is well described by a lognormal distribution for the
galaxies, the convergence and their joint PDF. We confirm that the galaxy
density contrast distribution is well modeled by a lognormal PDF convolved with
Poisson noise at angular scales from 10-40 arcmin (corresponding to physical
scales of 3-10 Mpc). We note that as kappa_WL is a weighted sum of the mass
fluctuations along the line of sight, its PDF is expected to be only
approximately lognormal. We find that the kappa_WL distribution is well modeled
by a lognormal PDF convolved with Gaussian shape noise at scales between 10 and
20 arcmin, with a best-fit chi^2/DOF of 1.11 compared to 1.84 for a Gaussian
model, corresponding to p-values 0.35 and 0.07 respectively, at a scale of 10
arcmin. Above 20 arcmin a simple Gaussian model is sufficient. The joint PDF is
also reasonably fitted by a bivariate lognormal. As a consistency check we
compare the variances derived from the lognormal modelling with those directly
measured via CiC. Our methods are validated against maps from the MICE Grand
Challenge N-body simulation.
