  Ballistic deposition is one of the many models of interface growth that are
believed to be in the KPZ universality class, but have so far proved to be
largely intractable mathematically. In this model, blocks of size one fall
independently as Poisson processes at each site on the $d$-dimensional lattice,
and either attach themselves to the column growing at that site, or to the side
of an adjacent column, whichever comes first. It is not hard to see that if we
subtract off the height of the column at the origin from the heights of the
other columns, the resulting interface process is Markovian. The main result of
this article is that this Markov process has at least one invariant probability
measure. We conjecture that the invariant measure is not unique, and provide
some partial evidence.
