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The distribution of the cosmic convergence field is modeled using alarge-deviation principle where all non-Gaussian contributions are computedfrom first principles. The geometry of the past light cone is accounted for byconstructing the total weak-lensing signal from contributions of the matterdensity in thin disk slices. The prediction of this model is successfullytested against numerical simulation with ray tracing, and found to be accuratewithin at least 5 per cent in the tails at redshift 1 and opening angle of 10arcmin and even more so with increasing source redshift and opening angle. Anaccurate analytical approximation to the theory is also provided for practicalimplementation. The lensing kernel that mixes physical scales along theline-of-sight tends to reduce the domain of validity of this theoreticalapproach compared to the three dimensional case of cosmic densities inspherical cells. This effect is shown to be avoidable if a nulling procedure isimplemented in order to localise the lensing line-of-sight integrations in atomographic analysis. Accuracy in the tails is thus achieved within a percentfor 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 issueof shape noise are discussed.

Game of cones: A nulling strategy for modelling lensing convergence in cones with large deviation theory