We study the weak gravitational lensing effects caused by a stochastic distribution of dark matter halos. We develop a simple approach to calculate the magnification probability distribution function which allows us to easily compute the magnitude bias and dispersion for an arbitrary data sample and a given universe model. As an application we consider the effects of single-mass large-scale cosmic inhomogeneities ($M\sim {10}^{15}{h}^{-1}{M}_{\odot }$) to the SNe magnitude-redshift relation, and conclude that such structures could bias the PDF enough to affect the extraction of cosmological parameters from the limited size of present-day SNe data samples. We also release $\mathtt{t}\mathtt{u}\mathtt{r}\mathtt{b}\mathtt{o}\mathtt{G}\mathtt{L}$ [$\mathtt{t}\mathtt{u}\mathtt{r}\mathtt{b}\mathtt{o}\mathtt{G}\mathtt{L}$ is available at: http://www.turbogl.org.], a simple and very fast ($\lesssim 1\mathrm{s}$) Mathematica code based on the method here presented.

• Received 14 September 2009

DOI:https://doi.org/10.1103/PhysRevD.80.123020