---
_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
arxiv: 1
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. <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>
  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.
  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.
corr_author: '1'
date_created: 2021-12-16T12:10:16Z
date_published: 2022-04-28T00:00:00Z
date_updated: 2024-10-09T21:01:17Z
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'
...