par Duerinckx, Mitia ;Fischer, Julian;Gloria, Antoine
Référence The Annals of applied probability, 32, 2, page (1179-1209)
Publication Publié, 2022-04-01
Article révisé par les pairs
Résumé : Consider a linear elliptic partial differential equation in divergence form with a random coefficient field. The solution-operator displays fluctuations around its expectation. The recently-developed pathwise theory of fluctuations in stochastic homogenization reduces the characterization of these fluctuations to those of the so-called standard homogenization commutator. In this contribution, we investigate the scaling limit of this key quantity: starting from a Gaussian-like coefficient field with possibly strong correlations, we establish the convergence of the rescaled commutator to a fractional Gaussian field, depending on the decay of correlations of the coefficient field, and we investigate the (non)degeneracy of the limit. This extends to general dimension d ≥ 1 previous results so far limited to dimension d = 1, and to the continuum setting with strong correlations recent results in the discrete i.i.d. case.