Tomography and Weak lensing Statistics
  Extending previous studies, we derive generic predictions for lower order
cumulants and their correlators for individual tomographic bins as well as
between two different bins. We derive the corresponding one- and two-point
joint probability distribution function for the tomographic convergence maps
from different bins as a function of angular smoothing scale. The modelling of
weak lensing statistics is obtained by adopting a detailed prescription for the
underlying density contrast. In this paper we concentrate on the convergence
field $\kappa$ and use top-hat filter; though the techniques presented can
readily be extended to model the PDF of shear components or to include other
windows such as the compensated filter. The functional form for the underlying
PDF and bias is modelled in terms of the non-linear or the quasilinear form
depending on the smoothing angular scale. Results from other semi-analytical
models e.g. the lognormal distribution are also presented. Introducing a
reduced convergence for individual bins, we are able to show that the
tomographic PDFs and bias for each bin sample the same functional form of the
underlying PDF of density contrast but with varying variance. The joint
probability distribution of the convergence maps that correspond to two
different tomographic bins can be constructed from individual tomographic PDF
and bias. We study their dependence on cosmological parameters for source
distributions corresponding to the realistic surveys such as LSST and DES. We
briefly outline how photometric redshift information can be incorporated in our
computation of cumulants, cumulant correlators and the PDFs. Connection of our
results to the full 3D calculations is elucidated. Analytical results for
inclusion of realistic noise and finite survey size are presented in detail.
