{"isi":1,"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_type":"original","publication_status":"published","oa":1,"oa_version":"Preprint","intvolume":"        32","department":[{"_id":"JuFi"}],"title":"Scaling limit of the homogenization commutator for Gaussian coefficient  fields","_id":"10548","volume":32,"date_updated":"2023-08-02T13:35:06Z","month":"04","page":"1179-1209","date_created":"2021-12-16T12:10:16Z","type":"journal_article","year":"2022","author":[{"first_name":"Mitia","last_name":"Duerinckx","full_name":"Duerinckx, Mitia"},{"last_name":"Fischer","full_name":"Fischer, Julian L","first_name":"Julian L","id":"2C12A0B0-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-0479-558X"},{"first_name":"Antoine","last_name":"Gloria","full_name":"Gloria, Antoine"}],"scopus_import":"1","doi":"10.1214/21-AAP1705","citation":{"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.” <i>Annals of Applied Probability</i>, vol. 32, no. 2, Institute of Mathematical Statistics, 2022, pp. 1179–209, doi:<a href=\"https://doi.org/10.1214/21-AAP1705\">10.1214/21-AAP1705</a>.","short":"M. Duerinckx, J.L. Fischer, A. Gloria, Annals of Applied Probability 32 (2022) 1179–1209.","apa":"Duerinckx, M., Fischer, J. L., &#38; Gloria, A. (2022). Scaling limit of the homogenization commutator for Gaussian coefficient  fields. <i>Annals of Applied Probability</i>. Institute of Mathematical Statistics. <a href=\"https://doi.org/10.1214/21-AAP1705\">https://doi.org/10.1214/21-AAP1705</a>","chicago":"Duerinckx, Mitia, Julian L Fischer, and Antoine Gloria. “Scaling Limit of the Homogenization Commutator for Gaussian Coefficient  Fields.” <i>Annals of Applied Probability</i>. Institute of Mathematical Statistics, 2022. <a href=\"https://doi.org/10.1214/21-AAP1705\">https://doi.org/10.1214/21-AAP1705</a>.","ieee":"M. Duerinckx, J. L. Fischer, and A. Gloria, “Scaling limit of the homogenization commutator for Gaussian coefficient  fields,” <i>Annals of applied probability</i>, vol. 32, no. 2. Institute of Mathematical Statistics, pp. 1179–1209, 2022.","ama":"Duerinckx M, Fischer JL, Gloria A. Scaling limit of the homogenization commutator for Gaussian coefficient  fields. <i>Annals of applied probability</i>. 2022;32(2):1179-1209. doi:<a href=\"https://doi.org/10.1214/21-AAP1705\">10.1214/21-AAP1705</a>"},"issue":"2","language":[{"iso":"eng"}],"article_processing_charge":"No","publisher":"Institute of Mathematical Statistics","abstract":[{"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.","lang":"eng"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","external_id":{"arxiv":["1910.04088"],"isi":["000791003700011"]},"quality_controlled":"1","publication":"Annals of applied probability","status":"public","day":"28","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1910.04088"}],"date_published":"2022-04-28T00:00:00Z","publication_identifier":{"issn":["1050-5164"]}}