We study the problem of characterizing the effective (homogenized) properties of materials whose diffusive properties are modeled with random fields. Focusing on elliptic PDEs with stationary and ergodic random coefficient functions, we provide a gentle introduction to the mathematical theory of homogenization of random media. We also present numerical examples to elucidate the theoretical concepts and results.
"Expository Paper: A primer on homogenization of elliptic PDEs with stationary and ergodic random coefficient functions." Rocky Mountain J. Math. 45 (3) 703 - 735, 2015. https://doi.org/10.1216/RMJ-2015-45-3-703