Probability distribution function of the aperture mass field with large
  deviation theory
  In the context of tomographic cosmic shear surveys, a theoretical model for
the one-point statistics of the aperture mass (Map) is developed. This
formalism is based on the application of the large deviation principle to the
projected matter density field and more specifically to the angular aperture
masses. The latter holds the advantage of being an observable that can be
directly extracted from the observed shear field and to be, by construction,
independent from the long wave modes. Furthermore we show that, with the help
of a nulling procedure based on the so-called BNT transform, it is possible to
build observables that depend only on a finite range of redshifts making them
also independent from the small-scale modes. This procedure makes predictions
for the shape of the one-point Probability Distribution Function of such an
observable very accurate, comparable to what had been previously obtained for
3D observables. Comparisons with specific simulations reveal however
inconsistent results showing that synthetic lensing maps were not accurate
enough for such refined observables. It points to the need for more precise
dedicated numerical developments whose performances could be benchmarked with
such observables. We furthermore review the possible systematics that could
affect such a formalism in future weak-lensing surveys like Euclid, notably the
impact of shape noise as well as leading corrections coming from lens-lens
couplings, geodesic deviation, reduced shear and magnification bias.
