  We prove a hydrodynamic limit for ballistic deposition on a multidimensional
lattice. In this growth model particles rain down at random and stick to the
growing cluster at the first point of contact. The theorem is that if the
initial random interface converges to a deterministic macroscopic function,
then at later times the height of the scaled interface converges to the
viscosity solution of a Hamilton-Jacobi equation. The proof idea is to
decompose the interface into the shapes that grow from individual seeds of the
initial interface. This decomposition converges to a variational formula that
defines viscosity solutions of the macrosopic equation. The technical side of
the proof involves subadditive methods and large deviation bounds for related
first-passage percolation processes.
