Homogenization and Corrector Theory for Linear Transport in Random Media

Guillaume Bal Department of Applied Physics and Applied Mathematics, Columbia University, New York NY, 10027 Wenjia Jing Department of Applied Physics and Applied Mathematics, Columbia University, New York, NY 10027, United States

Analysis of PDEs Probability mathscidoc:2206.03001

Discrete and Continuous Dynamical Systems, 28, (4), 1311-1343, 2010.12
We consider the theory of correctors to homogenization in stationary transport equations with rapidly oscillating, random coefficients. Let ε << 1 be the ratio of the correlation length in the random medium to the overall distance of propagation. As ε↓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.
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@inproceedings{guillaume2010homogenization,
  title={Homogenization and Corrector Theory for Linear Transport in Random Media},
  author={Guillaume Bal, and Wenjia Jing},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220622152056608997441},
  booktitle={Discrete and Continuous Dynamical Systems},
  volume={28},
  number={4},
  pages={1311-1343},
  year={2010},
}
Guillaume Bal, and Wenjia Jing. Homogenization and Corrector Theory for Linear Transport in Random Media. 2010. Vol. 28. In Discrete and Continuous Dynamical Systems. pp.1311-1343. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220622152056608997441.
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