  In this article, we study stochastic homogenization of non-homogeneous
Gaussian free fields $\Xi^{g,{\bf a}} $ and bi-Laplacian fields $\Xi^{b,{\bf
a}}$. They can be characterized as follows: for $f=\delta$ the solution $u$ of
$\nabla \cdot \mathbf{a} \nabla u =f$, ${\bf a}$ is a uniformly elliptic random
environment, is the covariance of $\Xi^{g,{\bf a}}$. When $f$ is the white
noise, the field $\Xi^{b,{\bf a}}$ can be viewed as the distributional solution
of the same elliptic equation. Our results characterize the scaling limit of
such fields on both, a sufficiently regular domain $D\subset \mathbb{R}^d$, or
on the discrete torus. Based on stochastic homogenization techniques applied to
the eigenfunction basis of the Laplace operator $\Delta$, we will show that
such families of fields converge to an appropriate multiple of the GFF resp.
bi-Laplacian. The limiting fields are determined by their respective
homogenized operator $\ahom \Delta$, with constant $\ahom$ depending on the law
of the environment ${\bf a}$. The proofs are based on the results found in
\cite{Armstrong2019} and \cite{gloria2014optimal}.
