---
_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'
...