Probability Distribution Functions of Cosmological Lensing: Convergence,
  Shear, and Magnification
  We perform high resolution ray-tracing simulations to investigate probability
distribution functions (PDFs) of lensing convergence, shear, and magnification
on distant sources up to the redshift of $z_s=20$. We pay particular attention
to the shot noise effect in $N$-body simulations by explicitly showing how it
affects the variance of the convergence. We show that the convergence and
magnification PDFs are closely related with each other via the approximate
relation $\mu=(1-\kappa)^{-2}$, which can reproduce the behavior of PDFs
surprisingly well up to the high magnification tail. The mean convergence
measured in the source plane is found to be systematically negative, rather
than zero as often assumed, and is correlated with the convergence variance. We
provide simple analytical formulae for the PDFs, which reproduce simulated PDFs
reasonably well for a wide range of redshifts and smoothing sizes. As explicit
applications of our ray-tracing simulations, we examine the strong lensing
probability and the magnification effects on the luminosity functions of
distant galaxies and quasars.
