  We study the homogenization limit of solutions to the G-equation with random
drift. This Hamilton-Jacobi equation is a model for flame propagation in a
turbulent fluid in the regime of thin flames. For a fluid velocity field that
is statistically stationary and ergodic, we prove sufficient conditions for
homogenization to hold with probability one. These conditions are expressed in
terms of travel times for the associated control problem. When the spatial
dimension is equal to two and the fluid velocity is divergence-free, we verify
that these conditions hold under suitable assumptions about the growth of the
random stream function.
