Luminosity distance in Swiss cheese cosmology with randomized voids. II.
  Magnification probability distributions
  We study the fluctuations in luminosity distances due to gravitational
lensing by large scale (> 35 Mpc) structures, specifically voids and sheets. We
use a simplified "Swiss cheese" model consisting of a \Lambda -CDM
Friedman-Robertson-Walker background in which a number of randomly distributed
non-overlapping spherical regions are replaced by mass compensating comoving
voids, each with a uniform density interior and a thin shell of matter on the
surface. We compute the distribution of magnitude shifts using a variant of the
method of Holz & Wald (1998), which includes the effect of lensing shear. The
standard deviation of this distribution is ~ 0.027 magnitudes and the mean is ~
0.003 magnitudes for voids of radius 35 Mpc, sources at redshift z_s=1.0, with
the voids chosen so that 90% of the mass is on the shell today. The standard
deviation varies from 0.005 to 0.06 magnitudes as we vary the void size, source
redshift, and fraction of mass on the shells today. If the shell walls are
given a finite thickness of ~ 1 Mpc, the standard deviation is reduced to ~
0.013 magnitudes. This standard deviation due to voids is a factor ~ 3 smaller
than that due to galaxy scale structures. We summarize our results in terms of
a fitting formula that is accurate to ~ 20%, and also build a simplified
analytic model that reproduces our results to within ~ 30%. Our model also
allows us to explore the domain of validity of weak lensing theory for voids.
We find that for 35 Mpc voids, corrections to the dispersion due to lens-lens
coupling are of order ~ 4%, and corrections to due shear are ~ 3%. Finally, we
estimate the bias due to source-lens clustering in our model to be negligible.
