Lensing in the Geodesic Light-Cone coordinates and its (exact)
  illustration to an off-center observer in Lema\^itre-Tolman-Bondi models
  We present in this paper a new application of the geodesic light-cone (GLC)
gauge for weak lensing calculations. Using interesting properties of this
gauge, we derive an exact expression of the amplification matrix - involving
convergence, magnification and shear - and of the deformation matrix -
involving the optical scalars. These expressions are simple and
non-perturbative as long as no caustics are created on the past light-cone and
are, by construction, free from the thin lens approximation. We apply these
general expressions on the example of an Lema\^itre-Tolman-Bondi (LTB) model
with an off-center observer and obtain explicit forms for the lensing
quantities as a direct consequence of the non-perturbative transformation
between GLC and LTB coordinates. We show their evolution in redshift after a
numerical integration, for underdense and overdense LTB models, and interpret
their respective variations in the simple non-curvature case.
