  Homogeneous fragmentations describe the evolution of a unit mass that breaks
down randomly into pieces as time passes. They can be thought of as continuous
time analogs of a certain type of branching random walks, which suggests the
use of time-discretization to shift known results from the theory of branching
random walks to the fragmentation setting. In particular, this yields
interesting information about the asymptotic behaviour of fragmentations.
  On the other hand, homogeneous fragmentations can also be investigated using
a powerful technique of discretization of space due to Kingman, namely, the
theory of exchangeable partitions of $\N$. Spatial discretization is especially
well-suited to develop directly for continuous times the conceptual method of
probability tilting of Lyons, Pemantle and Peres.
