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dc.contributor.authorBarchiesi, Marco
dc.contributor.authorJulin, Vesa
dc.date.accessioned2017-11-30T11:10:51Z
dc.date.available2018-05-05T21:45:05Z
dc.date.issued2017
dc.identifier.citationBarchiesi, M., & Julin, V. (2017). Robustness of the Gaussian concentration inequality and the Brunn–Minkowski inequality. <em>Calculus of Variations and Partial Differential Equations</em>, 56 (3), 80. <a href="https://doi.org/10.1007/s00526-017-1169-x">doi:10.1007/s00526-017-1169-x</a>
dc.identifier.otherTUTKAID_73716
dc.identifier.urihttps://jyx.jyu.fi/handle/123456789/56064
dc.description.abstractWe provide a sharp quantitative version of the Gaussian concentration inequality: for every r > 0, the difference between the measure of the r-enlargement of a given set and the r-enlargement of a half-space controls the square of the measure of the symmetric difference between the set and a suitable half-space. We also prove a similar estimate in the Euclidean setting for the enlargement with a general convex set. This is equivalent to the stability of the Brunn-Minkowski inequality for the Minkowski sum between a convex set and a generic one.
dc.language.isoeng
dc.publisherSpringer
dc.relation.ispartofseriesCalculus of Variations and Partial Differential Equations
dc.subject.othermathematics
dc.subject.otherGaussian concentration inequality
dc.subject.otherquantitative research
dc.subject.otherBrunn–Minkowski inequality
dc.titleRobustness of the Gaussian concentration inequality and the Brunn–Minkowski inequality
dc.typearticle
dc.identifier.urnURN:NBN:fi:jyu-201711294417
dc.contributor.laitosMatematiikan ja tilastotieteen laitosfi
dc.contributor.laitosDepartment of Mathematics and Statisticsen
dc.contributor.oppiaineMatematiikka
dc.type.urihttp://purl.org/eprint/type/JournalArticle
dc.date.updated2017-11-29T10:15:17Z
dc.type.coarjournal article
dc.description.reviewstatuspeerReviewed
dc.relation.issn0944-2669
dc.relation.volume56
dc.type.versionacceptedVersion
dc.rights.copyright© Springer-Verlag Berlin Heidelberg 2017. This is a final draft version of an article whose final and definitive form has been published by Springer. Published in this repository with the kind permission of the publisher.
dc.rights.accesslevelopenAccessfi
dc.relation.doi10.1007/s00526-017-1169-x


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