Scaling limit of the homogenization commutator for Gaussian coefficient fields

Consider a linear elliptic partial differential equation in divergence form with random coefficient field. The solution-operator displays fluctuations around its expectation. recently-developed pathwise theory of stochastic homogenization reduces the characterization these to those so-called standard commutator. In this contribution, we investigate scaling limit key quantity: starting from Gaussian-like field possibly strong correlations, establish convergence rescaled commutator fractional Gaussian field, depending on decay correlations and (non)degeneracy limit. This extends general dimension d≥1 previous results so far limited d=1, continuum setting recent discrete i.i.d. case.