Simulations of Wide-Field Weak Lensing Surveys I: Basic Statistics and
  Non-Gaussian Effects
  We study the lensing convergence power spectrum and its covariance for a
standard LCDM cosmology. We run 400 cosmological N-body simulations and use the
outputs to perform a total of 1000 independent ray-tracing simulations. We
compare the simulation results with analytic model predictions. The
semi-analytic model based on Smith et al.(2003) fitting formula underestimates
the convergence power by ~30% at arc-minute angular scales. For the convergence
power spectrum covariance, the halo model reproduces the simulation results
remarkably well over a wide range of angular scales and source redshifts. The
dominant contribution at small angular scales comes from the sample variance
due to the number fluctuations of halos in a finite survey volume. The
signal-to-noise ratio for the convergence power spectrum is degraded by the
non-Gaussian covariances by up to a factor 5 for a weak lensing survey to z_s
~1. The probability distribution of the convergence power spectrum estimators,
among the realizations, is well approximated by a chi-square distribution with
broadened variance given by the non-Gaussian covariance, but has a larger
positive tail. The skewness and kurtosis have non-negligible values especially
for a shallow survey. We argue that a prior knowledge on the full distribution
may be needed to obtain an unbiased estimate on the ensemble averaged band
power at each angular scale from a finite volume survey.
