Homogenization and corrector theory for lineartransport in random media

Abstract

We consider the theory of correctors to homogenization in stationarytransport equations with rapidly oscillating, random coefficients.Let ε << 1 be the ratio of the correlation length in the randommedium to the overall distance of propagation. As ε $ \downarrow0$, we show that the heterogeneous transport solution iswell-approximated by a homogeneous transport solution. We then showthat the rescaled corrector converges in (probability) distributionand weakly in the space and velocity variables, to a Gaussianprocess as an application of a central limit result. The latterresult requires strong assumptions on the statistical structure ofrandomness and is proved for random processes constructed bymeans of a Poisson point process.