Accurate Modeling of Weak Lensing with the sGL Method
  We revise and extend the stochastic approach to cumulative weak lensing
(hereafter the sGL method) first introduced in Ref. [1]. Here we include a
realistic halo mass function and density profiles to model the distribution of
mass between and within galaxies, galaxy groups and galaxy clusters. We also
introduce a modeling of the filamentary large-scale structures and a method to
embed halos into these structures. We show that the sGL method naturally
reproduces the weak lensing results for the Millennium Simulation. The strength
of the sGL method is that a numerical code based on it can compute the lensing
probability distribution function for a given inhomogeneous model universe in a
few seconds. This makes it a useful tool to study how lensing depends on
cosmological parameters and its impact on observations. The method can also be
used to simulate the effect of a wide array of systematic biases on the
observable PDF. As an example we show how simple selection effects may reduce
the variance of observed PDF, which could possibly mask opposite effects from
very large scale structures. We also show how a JDEM-like survey could
constrain the lensing PDF relative to a given cosmological model. The updated
turboGL code is available at turboGL.org.
