  We review the factorization of the $S$-matrix elements in the context of
particle scattering off an external field, which can serve as a model for the
field of a large nucleus. The factorization takes the form of a convolution of
light cone wave functions describing the physical incoming and outgoing states
in terms of bare partons, and products of Wilson lines. The latter represent
the interaction between the bare partons and the external field. Specializing
to elastic scattering amplitudes of onia at very high energies, we introduce
the color dipole model, which formulates the calculation of the modulus-squared
of the wave functions in quantum chromodynamics with the help of a branching
random walk, and the scattering amplitudes as observables on this classical
stochastic process. Methods developed for general branching processes produce
analytical formulas for the asymptotics of such observables, and thus enable
one to derive exact large-rapidity expressions for onium-nucleus cross
sections, from which electron-nucleus cross sections may be inferred.
