  We are interested in the averaged behavior of interfaces moving in stationary
ergodic environments, with oscillatory normal velocity which changes sign. This
problem can be reformulated, using level sets, as the homogenization of a
Hamilton-Jacobi equation with a positively homogeneous non-coercive
Hamiltonian. The periodic setting was earlier studied by Cardaliaguet, Lions
and Souganidis (2009). Here we concentrate in the random media and show that
the solutions of the oscillatory Hamilton-Jacobi equation converge in
$L^\infty$-weak $*$ to a linear combination of the initial datum and the
solutions of several initial value problems with deterministic effective
Hamiltonian(s), determined by the properties of the random media.
