HOMOGENIZATION AND CORRECTOR THEORY FOR LINEAR TRANSPORT IN RANDOM MEDIA

We consider the theory of correctors to homogenization in stationary transport equations with rapidly oscillating, random coefficients. Let epsilon << 1 be the ratio of the correlation length in the random medium to the overall distance of propagation. As epsilon down arrow 0, we show that the heterogeneous transport solution is well-approximated by a homogeneous transport solution. We then show that the rescaled corrector converges in (probability) distribution and weakly in the space and velocity variables, to a Gaussian process as an application of a central limit result. The latter result requires strong assumptions on the statistical structure of randomness and is proved for random processes constructed by means of a Poisson point process.