  The statistical property of the weak lensing fields is studied quantitatively
using the ray-tracing simulations. Motivated by the empirical lognormal model
that characterizes the probability distribution function(PDF) of the
three-dimensional mass distribution excellently, we critically investigate the
validity of lognormal model in the weak lensing statistics. Assuming that the
convergence field, $\kappa$, is approximately described by the lognormal
distribution, we present analytic formulae of convergence for the one-point PDF
and the Minkowski functionals. Comparing those predictions with ray-tracing
simulations in various cold dark matter models, we find that the one-point
lognormal PDF can describe the non-Gaussian tails of convergence fields
accurately up to $\nu\sim10$, where $\nu$ is the level threshold given by
$\nu\equiv\kappa/\var^{1/2}$, although the systematic deviation from lognormal
prediction becomes manifest at higher source redshift and larger smoothing
scales. The lognormal formulae for Minkowski functionals also fit to the
simulation results when the source redshift is low. Accuracy of the
lognormal-fit remains good even at the small angular scales, where the
perturbation formulae by Edgeworth expansion break down. On the other hand,
lognormal models does not provide an accurate prediction for the statistics
sensitive to the rare events such as the skewness and the kurtosis of
convergence. We therefore conclude that the empirical lognormal model of the
convergence field is safely applicable as a useful cosmological tool, as long
as we are concerned with the non-Gaussianity of $\nu\simlt5$ for low source
redshift samples.

Astrophysics