  We present stochastic homogenization results for viscous Hamilton-Jacobi
equations using a new argument which is based only on the subadditive structure
of maximal subsolutions (solutions of the "metric problem"). This permits us to
give qualitative homogenization results under very general hypotheses: in
particular, we treat non-uniformly coercive Hamiltonians which satisfy instead
a weaker averaging condition. As an application, we derive a general quenched
large deviations principle for diffusions in random environments and with
absorbing random potentials.
