### On a variant of random homogenization theory: convergence of the residual process and approximation of the homogenized coefficients

We consider the variant of stochastic homogenization theory introduced in [X. Blanc, C. Le Bris and P.-L. Lions, 343 (2006) 717–724.; X. Blanc, C. Le Bris and P.-L. Lions, 88 (2007) 34–63.]. The equation under consideration is a standard linear elliptic equation in divergence form, where the highly oscillatory coefficient is the composition of a periodic matrix with a stochastic diffeomorphism. The homogenized limit of this problem has been identified in [X. Blanc, C. Le Bris and P.-L. Lions, 343...