Game of cones: A nulling strategy for modelling lensing convergence in
  cones with large deviation theory
  The distribution of the cosmic convergence field is modeled using a
large-deviation principle where all non-Gaussian contributions are computed
from first principles. The geometry of the past light cone is accounted for by
constructing the total weak-lensing signal from contributions of the matter
density in thin disk slices. The prediction of this model is successfully
tested against numerical simulation with ray tracing, and found to be accurate
within at least 5 per cent in the tails at redshift 1 and opening angle of 10
arcmin and even more so with increasing source redshift and opening angle. An
accurate analytical approximation to the theory is also provided for practical
implementation. The lensing kernel that mixes physical scales along the
line-of-sight tends to reduce the domain of validity of this theoretical
approach compared to the three dimensional case of cosmic densities in
spherical cells. This effect is shown to be avoidable if a nulling procedure is
implemented in order to localise the lensing line-of-sight integrations in a
tomographic analysis. Accuracy in the tails is thus achieved within a percent
for source redshifts between 0.5 and 1.5 and an opening angle of 10 arcmin.
Applications to future weak-lensing surveys like Euclid and the specific issue
of shape noise are discussed.
