  We consider particles on a one-dimensional lattice whose evolution is
governed by nearest-neighbor interactions where particles that have reached
size zero are removed from the system. Concentrating on configurations with
infinitely many particles, we prove existence of solutions under a reasonable
density assumption on the initial data and show that the vanishing of particles
and the localized interactions can lead to non-uniqueness. Moreover, we provide
a rigorous upper coarsening estimate and discuss the generic statistical
properties as well as some non-generic behavior of the evolution by means of
heuristic arguments and numerical observations.
