Scaling limit of the homogenization commutator for Gaussian coefficient fields
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.
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https://arxiv.org/abs/1910.04088
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Journal Article
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| English
Scopus indexed
Author
Duerinckx, Mitia;
Fischer, Julian LISTA ;
Gloria, Antoine
Department
Abstract
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 $d\ge1$ previous results so far limited to dimension $d=1$, and to the continuum setting with strong correlations recent results in the discrete iid case.
Publishing Year
Date Published
2022-04-28
Journal Title
Annals of applied probability
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).
Volume
32
Issue
2
Page
1179-1209
ISSN
IST-REx-ID
Cite this
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
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
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.
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.
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.
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.
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arXiv 1910.04088