--- _id: '10548' abstract: - lang: eng text: "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\r\nfrom 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\r\ninvestigate the (non)degeneracy of the limit. This extends to general dimension $d\\ge1$ previous results so far limited to dimension $d=1$, and to the continuum setting with strong correlations recent results in the discrete iid case." acknowledgement: The authors thank Ivan Nourdin and Felix Otto for inspiring discussions. The work of MD is financially supported by the CNRS-Momentum program. Financial support of AG is acknowledged from the European Research Council under the European Community’s Seventh Framework Programme (FP7/2014-2019 Grant Agreement QUANTHOM 335410). article_processing_charge: No article_type: original author: - first_name: Mitia full_name: Duerinckx, Mitia last_name: Duerinckx - first_name: Julian L full_name: Fischer, Julian L id: 2C12A0B0-F248-11E8-B48F-1D18A9856A87 last_name: Fischer orcid: 0000-0002-0479-558X - first_name: Antoine full_name: Gloria, Antoine last_name: Gloria citation: ama: Duerinckx M, Fischer JL, Gloria A. Scaling limit of the homogenization commutator for Gaussian coefficient  fields. Annals of applied probability. 2022;32(2):1179-1209. doi:10.1214/21-AAP1705 apa: Duerinckx, M., Fischer, J. L., & Gloria, A. (2022). Scaling limit of the homogenization commutator for Gaussian coefficient  fields. Annals of Applied Probability. Institute of Mathematical Statistics. https://doi.org/10.1214/21-AAP1705 chicago: Duerinckx, Mitia, Julian L Fischer, and Antoine Gloria. “Scaling Limit of the Homogenization Commutator for Gaussian Coefficient  Fields.” Annals of Applied Probability. Institute of Mathematical Statistics, 2022. https://doi.org/10.1214/21-AAP1705. ieee: M. Duerinckx, J. L. Fischer, and A. Gloria, “Scaling limit of the homogenization commutator for Gaussian coefficient  fields,” Annals of applied probability, vol. 32, no. 2. Institute of Mathematical Statistics, pp. 1179–1209, 2022. ista: Duerinckx M, Fischer JL, Gloria A. 2022. Scaling limit of the homogenization commutator for Gaussian coefficient  fields. Annals of applied probability. 32(2), 1179–1209. mla: Duerinckx, Mitia, et al. “Scaling Limit of the Homogenization Commutator for Gaussian Coefficient  Fields.” Annals of Applied Probability, vol. 32, no. 2, Institute of Mathematical Statistics, 2022, pp. 1179–209, doi:10.1214/21-AAP1705. short: M. Duerinckx, J.L. Fischer, A. Gloria, Annals of Applied Probability 32 (2022) 1179–1209. date_created: 2021-12-16T12:10:16Z date_published: 2022-04-28T00:00:00Z date_updated: 2023-08-02T13:35:06Z day: '28' department: - _id: JuFi doi: 10.1214/21-AAP1705 external_id: arxiv: - '1910.04088' isi: - '000791003700011' intvolume: ' 32' isi: 1 issue: '2' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1910.04088 month: '04' oa: 1 oa_version: Preprint page: 1179-1209 publication: Annals of applied probability publication_identifier: issn: - 1050-5164 publication_status: published publisher: Institute of Mathematical Statistics quality_controlled: '1' scopus_import: '1' status: public title: Scaling limit of the homogenization commutator for Gaussian coefficient fields type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 32 year: '2022' ...