  We describe an efficient algorithm for calculating the statistics of weak
lensing by large-scale structure based on a tiled set of independent
particle-mesh N-body simulations which telescope in resolution along the line
of sight. This efficiency allows us to predict not only the mean properties of
lensing observables such as the power spectrum, skewness and kurtosis of the
convergence, but also their sampling errors for finite fields of view, which
are themselves crucial for assessing the cosmological significance of
observations. We find that the nongaussianity of the distribution substantially
increases the sampling errors for the skewness and kurtosis in the several to
tens of arcminutes regime, whereas those for the power spectrum are only
fractionally increased even out to wavenumbers where shot noise from the
intrinsic ellipticities of the galaxies will likely dominate the errors.
