A brief note on stochastic homogenization in 1D
Alen Alexanderian · 2013
In this brief note, we discuss the homogenization of a 1D elliptic operator with a random coefficient function. As is generally well-known, under assumptions of stationarity and ergodicity, there is a closed form expression for the homogenized coefficient in 1D. We provide a simple derivation of this result and also discuss the connections to the general theoretical framework in [4]. We also discuss the method of periodization in the 1D case and provide some numerical examples.