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Scaling limit of the homogenization commutator for Gaussian coefficient fields

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 نشر من قبل Antoine Gloria
 تاريخ النشر 2019
  مجال البحث
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Consider a linear elliptic partial differential equation in divergence form with a random coefficient field. The solution-operator displays fluctuations around itsexpectation. 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 $dge 1$ previous results so far limited to dimension $d=1$.



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