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dc.contributor.authorArmstrong, Scott N.*
dc.contributor.authorCardaliaguet, Pierre*
dc.contributor.authorSouganidis, Panagiotis E.*
dc.date.accessioned2012-07-04T14:26:18Z
dc.date.available2012-07-04T14:26:18Z
dc.date.issued2014
dc.identifier.issn0894-0347
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/9695
dc.language.isoenen
dc.subjectconvergence rate
dc.subjectfirst-passage percolation
dc.subjectHamilton-Jacobi equation
dc.subjecterror estimate
dc.subjectstochastic homogenization
dc.subject.ddc519en
dc.titleError estimates and convergence rates for the stochastic homogenization of Hamilton-Jacobi equations
dc.typeArticle accepté pour publication ou publié
dc.contributor.editoruniversityotherDepartment of Mathematics [Chicago] http://math.uchicago.edu/ University of Chicago;États-Unis
dc.contributor.editoruniversityotherDepartment of Mathematics [Madison] http://www.math.wisc.edu University of Wisconsin, Madison;États-Unis
dc.description.abstractenWe present exponential error estimates and demonstrate an algebraic convergence rate for the homogenization of level-set convex Hamilton-Jacobi equations in i.i.d. random environments, the first quantitative homogenization results for these equations in the stochastic setting. By taking advantage of a connection between the metric approach to homogenization and the theory of first-passage percolation, we obtain estimates on the fluctuations of the solutions to the approximate cell problem in the ballistic regime (away from flat spot of the effective Hamiltonian). In the sub-ballistic regime (on the flat spot), we show that the fluctuations are governed by an entirely different mechanism and the homogenization may proceed, without further assumptions, at an arbitrarily slow rate. We identify a necessary and sufficient condition on the law of the Hamiltonian for an algebraic rate of convergence to hold in the sub-ballistic regime and show, under this hypothesis, that the two rates may be merged to yield comprehensive error estimates and an algebraic rate of convergence for homogenization. Our methods are novel and quite different from the techniques employed in the periodic setting, although we benefit from previous works in both first-passage percolation and homogenization. The link between the rate of homogenization and the flat spot of the effective Hamiltonian, which is related to the nonexistence of correctors, is a purely random phenomenon observed here for the first time.
dc.relation.isversionofjnlnameJournal of the American Mathematical Society
dc.relation.isversionofjnlvol27
dc.relation.isversionofjnldate2014
dc.relation.isversionofjnlpages479-540
dc.relation.isversionofdoihttp://dx.doi.org/10.1090/S0894-0347-2014-00783-9
dc.description.sponsorshipprivateouien
dc.relation.isversionofjnlpublisherAmerican Mathematical Society
dc.subject.ddclabelProbabilités et mathématiques appliquéesen
dc.description.ssrncandidatenon
dc.description.halcandidateoui
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dc.description.audienceInternational
dc.relation.Isversionofjnlpeerreviewedoui
dc.date.updated2019-02-22T10:28:42Z
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