Higher-order Convergence Statistics for Three-dimensional Weak
  Gravitational Lensing
  Weak gravitational lensing on a cosmological scales can provide strong
constraints both on the nature of dark matter and the dark energy equation of
state. Most current weak lensing studies are restricted to (two-dimensional)
projections, but tomographic studies with photometric redshifts have started,
and future surveys offer the possibility of probing the evolution of structure
with redshift. In future we will be able to probe the growth of structure in 3D
and put tighter constraints on cosmological models than can be achieved by the
use of galaxy redshift surveys alone. Earlier studies in this direction focused
mainly on evolution of the 3D power spectrum, but extension to higher-order
statistics can lift degeneracies as well as providing information on primordial
non-gaussianity. We present analytical results for specific higher-order
descriptors, the bispectrum and trispectrum, as well as collapsed multi-point
statistics derived from them, i.e. cumulant correlators. We also compute
quantities we call the power spectra associated with the bispectrum and
trispectrum, the Fourier transforms of the well-known cumulant correlators. We
compute the redshift dependence of these objects and study their performance in
the presence of realistic noise and photometric redshift errors.
