Construction of the one-point PDF of the local aperture mass in weak lensing maps

We present a general method for the reconstruction of the one-point Probability Distribution Function of the local aperture mass in weak lensing maps. Exact results, that neglect the lens-lens coupling and departure from the Born approximation, are derived for both the quasilinear regime at leading order and the strongly nonlinear regime assuming the tree hierarchical model is valid. We describe in details the projection effects on the properties of the PDF and the associated generating functions. In particular, we show how the generic features which are common to both the quasilinear and nonlinear regimes lead to two exponential tails for P(M_ap). We briefly investigate the dependence of the PDF with cosmology and with the shape of the angular filter. Our predictions are seen to agree reasonably well with the results of numerical simulations and should be able to serve as foundations for alternative methods to measure the cosmological parameters that take advantage of the full shape of the PDF.