Homogenization and corrector theory for lineartransport in random media

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