Cosmic statistics through weak lenses

Many recent studies have demonstrated that scaling arguments, such as the so-called hierarchical ansatz, are extremely useful in understanding the statistical properties of weak gravitational lensing. This is especially true on small angular scales (i.e. at high resolution), where the usual perturbative calculations of matter clustering no longer apply. We build on these studies in order to develop a complete picture of weak lensing at small smoothing angles. In particular, we study the full probability distribution function, bias and other multipoint statistics for the 'hot spots' of the convergence field induced by weak lensing, and relate these to the statistics of overdense regions in the underlying mass distribution. It is already known that weak lensing can constrain the background geometry of the Universe, but we further show that it can also provide valuable information about the statistics of collapsed objects and the physics of collisionless clustering. Our results are particularly important for future observations which will, at least initially, focus on small smoothing angles.