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Functional Inequalities for Two-Level Concentration

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dc.abstract.enProbability measures satisfying a Poincaré inequality are known to enjoy a dimension-free concentration inequality with exponential rate. A celebrated result of Bobkov and Ledoux shows that a Poincaré inequality automatically implies a modified logarithmic Sobolev inequality. As a consequence the Poincaré inequality ensures a stronger dimension-free concentration property, known as two-level concentration. We show that a similar phenomenon occurs for the Latała–Oleszkiewicz inequalities, which were devised to uncover dimension-free concentration with rate between exponential and Gaussian. Motivated by the search for counterexamples to related questions, we also develop analytic techniques to study functional inequalities for probability measures on the line with wild potentials.
dc.affiliationUniwersytet Warszawski
dc.contributor.authorBarthe, Franck
dc.contributor.authorStrzelecki, Michał
dc.date.accessioned2024-01-25T01:40:20Z
dc.date.available2024-01-25T01:40:20Z
dc.date.copyright2021-07-03
dc.date.issued2022
dc.description.accesstimeAT_PUBLICATION
dc.description.financePublikacja bezkosztowa
dc.description.versionFINAL_PUBLISHED
dc.description.volume56
dc.identifier.doi10.1007/S11118-021-09900-9
dc.identifier.issn0926-2601
dc.identifier.urihttps://repozytorium.uw.edu.pl//handle/item/107621
dc.identifier.weblinkhttps://doi.org/10.1007/s11118-021-09900-9
dc.languageeng
dc.pbn.affiliationmathemathics
dc.relation.ispartofPotential Analysis
dc.relation.pages669–696
dc.rightsCC-BY
dc.sciencecloudnosend
dc.subject.enBeckner-type inequalities
dc.subject.enConcentration of measure
dc.subject.enModified log-Sobolev inequalities
dc.titleFunctional Inequalities for Two-Level Concentration
dc.typeJournalArticle
dspace.entity.typePublication