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dc.contributor.authorArmstrong, Scott N.*
hal.structure.identifier
dc.contributor.authorKuusi, Tuomo*
hal.structure.identifier
dc.contributor.authorMourrat, Jean-Christophe*
dc.date.accessioned2017-11-24T15:42:11Z
dc.date.available2017-11-24T15:42:11Z
dc.date.issued2017
dc.identifier.issn0020-9910
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/17044
dc.language.isoenen
dc.subjectstochastic homogenization
dc.subjecterror estimates
dc.subjectregularity theory
dc.subjectrenormalization
dc.subjectscaling limits
dc.subjectGaussian free field
dc.subject.ddc515en
dc.titleThe additive structure of elliptic homogenization
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenOne of the principal difficulties in stochastic homogenization is transferring quantitative ergodic information from the coefficients to the solutions, since the latter are nonlocal functions of the former. In this paper, we address this problem in a new way, in the context of linear elliptic equations in divergence form, by showing that certain quantities associated to the energy density of solutions are essentially additive. As a result, we are able to prove quantitative estimates on the weak convergence of the gradients, fluxes and energy densities of the first-order correctors (under blow-down) which are optimal in both scaling and stochastic integrability. The proof of the additivity is a bootstrap argument, completing the program initiated in Armstrong et al. (Commun. Math. Phys. 347(2):315–361, 2016): using the regularity theory recently developed for stochastic homogenization, we reduce the error in additivity as we pass to larger and larger length scales. In the second part of the paper, we use the additivity to derive central limit theorems for these quantities by a reduction to sums of independent random variables. In particular, we prove that the first-order correctors converge, in the large-scale limit, to a variant of the Gaussian free field.
dc.relation.isversionofjnlnameInventiones Mathematicae
dc.relation.isversionofjnlvol208
dc.relation.isversionofjnlissue3
dc.relation.isversionofjnldate2017
dc.relation.isversionofjnlpages999–1154
dc.relation.isversionofdoi10.1007/s00222-016-0702-4
dc.relation.isversionofjnlpublisherSpringer
dc.subject.ddclabelAnalyseen
dc.relation.forthcomingnonen
dc.relation.forthcomingprintnonen
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dc.description.audienceInternational
dc.relation.Isversionofjnlpeerreviewedoui
dc.date.updated2017-12-15T15:26:13Z
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