  Weak lensing surveys are expected to provide direct measurements of the
statistics of the projected dark matter distribution. Most analytical studies
of weak lensing statistics have been limited to quasilinear scales as they
relied on perturbative calculations. On the other hand, observational surveys
are likely to probe angular scales less than 10 arcminutes, for which the
relevant physical length scales are in the nonlinear regime of gravitational
clustering. We use the hierarchical ansatz to compute the multi-point
statistics of the weak lensing convergence for these small smoothing angles. We
predict the multi-point cumulants and cumulant correlators up to fourth order
and compare our results with high resolution ray tracing simulations. Averaging
over a large number of simulation realizations for four different cosmological
models, we find close agreement with the analytical calculations. In
combination with our work on the probability distribution function, these
results provide accurate analytical models for the full range of weak lensing
statistics. The models allow for a detailed exploration of cosmological
parameter space and of the dependence on angular scale and the redshift
distribution of source galaxies. We compute the dependence of the higher
moments of the convergence on the parameters Omega and Lambda and on the nature
of gravitational clustering.
