  We consider the homogenization of monotone systems of viscous Hamilton-Jacobi
equations with convex nonlinearities set in the stationary, ergodic setting.
The primary focus of this paper is on collapsing systems which, as the
microscopic scale tends to zero, average to a deterministic scalar
Hamilton-Jacobi equation. However, our methods also apply to systems which do
not collapse and, as the microscopic scale tends to zero, average to a
deterministic system of Hamilton-Jacobi equations.
