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dc.contributor.authorGonçalves, Patricia
dc.contributor.authorJara, Milton
dc.date.accessioned2014-01-10T14:38:00Z
dc.date.available2014-01-10T14:38:00Z
dc.date.issued2014
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/12388
dc.language.isoenen
dc.subjectenergy solutions of the stochastic Burgers equationen
dc.subjectenergy solutions of the KPZ equationen
dc.subjectsecond-order Boltzmann–Gibbs principleen
dc.subject.ddc519en
dc.titleNonlinear Fluctuations of Weakly Asymmetric Interacting Particle Systemsen
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenWe introduce what we call the second-order Boltzmann–Gibbs principle, which allows one to replace local functionals of a conservative, one-dimensional stochastic process by a possibly nonlinear function of the conserved quantity. This replacement opens the way to obtain nonlinear stochastic evolutions as the limit of the fluctuations of the conserved quantity around stationary states. As an application of this second-order Boltzmann–Gibbs principle, we introduce the notion of energy solutions of the KPZ and stochastic Burgers equations. Under minimal assumptions, we prove that the density fluctuations of one-dimensional, stationary, weakly asymmetric, conservative particle systems are sequentially compact and that any limit point is given by energy solutions of the stochastic Burgers equation. We also show that the fluctuations of the height function associated to these models are given by energy solutions of the KPZ equation in this sense. Unfortunately, we lack a uniqueness result for these energy solutions. We conjecture these solutions to be unique, and we show some regularity results for energy solutions of the KPZ/Burgers equation, supporting this conjecture.en
dc.relation.isversionofjnlnameArchive for Rational Mechanics and Analysis
dc.relation.isversionofjnlvol212
dc.relation.isversionofjnlissue2
dc.relation.isversionofjnldate2014
dc.relation.isversionofjnlpages597-644
dc.relation.isversionofdoihttp://dx.doi.org/10.1007/s00205-013-0693-xen
dc.identifier.urlsitehttp://arxiv.org/abs/1309.5120v1en
dc.relation.isversionofjnlpublisherSpringeren
dc.subject.ddclabelProbabilités et mathématiques appliquéesen


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