SCALING LIMIT OF THE HOMOGENIZATION COMMUTATOR FOR GAUSSIAN COEFFICIENT FIELDS

• 成果类型: Article
• 署名作者: Duerinckx, Mitia; Fischer, Julian; Gloria, Antoine
• 署名单位: Universite Libre de Bruxelles; Institute of Science & Technology - Austria; Sorbonne Universite; Universite Paris Cite
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/21-AAP1705
• 发表日期: 2022
• 页码: 1179-1209
• 关键词: stochastic homogenization; INTEGRALS; fluctuations; CONVERGENCE; corrector

摘要

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 >= 1 previous results so far limited to dimension d = 1, and to the continuum setting with strong correlations recent results in the discrete i.i.d. case.