  Weak gravitational lensing, resulting from the bending of light due to the
presence of matter along the line of sight, is a potent tool for exploring
large-scale structures, particularly in quantifying non-Gaussianities. It
stands as a pivotal objective for upcoming surveys. In the realm of current and
forthcoming full-sky weak-lensing surveys, the convergence maps, representing a
line-of-sight integration of the matter density field up to the source
redshift, facilitate field-level inference, providing an advantageous avenue
for cosmological exploration. Traditional two-point statistics fall short of
capturing non-Gaussianities, necessitating the use of higher-order statistics
to extract this crucial information. Among the various higher-order statistics
available, the wavelet $\ell_1$-norm has proven its efficiency in inferring
cosmology (Ajani et al.2021). However, the lack of a robust theoretical
framework mandates reliance on simulations, demanding substantial resources and
time. Our novel approach introduces a theoretical prediction of the wavelet
$\ell_1$-norm for weak lensing convergence maps, grounded in the principles of
Large-Deviation theory. We present, for the first time, a theoretical
prediction of the wavelet $\ell_1$-norm for convergence maps, derived from the
theoretical prediction of their one-point probability distribution.
Additionally, we explore the cosmological dependence of this prediction and
validate the results on simulations. A comparison of our predicted wavelet
$\ell_1$-norm with simulations demonstrates a high level of accuracy in the
weakly non-linear regime. Moreover, we show its ability to capture cosmological
dependence, paving the way for a more robust and efficient parameter inference
process.
