  The real-space renormalization procedures on hierarchical lattices have been
much studied for many disordered systems in the past at the level of their
typical fluctuations. In the present paper, the goal is to analyze instead the
renormalization flows for the tails of probability distributions in order to
extract the scalings of their large deviations and the tails behaviors of the
corresponding rate functions. We focus on the renormalization rule for the
ground-state energy of the Directed Polymer model in a random medium, and study
the various renormalization flows that can emerge for the tails as a function
of the tails of the initial condition.
