  The aperture mass has been shown in a series of recent publications to be a
useful quantitative tool for weak lensing studies, ranging from cosmic shear to
the detection of a mass-selected sample of dark matter haloes. Quantitative
analytical predictions for the aperture mass have been based on a number of
simplifying assumptions. In this paper, we test the reliability of these
assumptions and the quality of the analytic approximations, using ray-tracing
simulations through a cosmological density field generated by very large N-body
simulations. We find that those analytic predictions which take into account
the non-linear evolution of the matter distribution, such as the dispersion of
the aperture mass and the halo abundance, are surprisingly accurately
reproduced with our numerical results, whereas the predictions for the
skewness, based on quasi-linear theory, are rather imprecise. In particular, we
verify numerically that the probability distribution of the aperture mass
decreases exponentially for values much larger than the rms. Given the good
overall agreement, comparisons between the observed distribution of the
aperture mass and the theoretical values provide a powerful tool for testing
cosmological models.
