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Modified logarithmic Sobolev inequalities and transportation inequalities

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Date
2005
Link to item file
http://hal.archives-ouvertes.fr/hal-00001609/en/
Dewey
Probabilités et mathématiques appliquées
Sujet
Logarithmic Sobolev inequality; Poincaré inequality; Hardy inequality
Journal issue
Probability Theory and Related Fields
Volume
133
Number
3
Publication date
11-2005
Article pages
409-436
DOI
http://dx.doi.org/10.1007/s00440-005-0432-9
URI
https://basepub.dauphine.fr/handle/123456789/557
Collections
  • CEREMADE : Publications
Metadata
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Author
Gentil, Ivan
Guillin, Arnaud
Miclo, Laurent
Type
Article accepté pour publication ou publié
Abstract (EN)
We present a new class of modified logarithmic Sobolev inequality, interpolating between Poincaré and logarithmic Sobolev inequalities, suitable for measures of the type $\exp(-|x|^\al)$ or $\exp(-|x|^\al\log^\beta(2+|x|))$ ($\al\in]1,2[$ and $\be\in\dR$) which lead to new concentration inequalities. These modified inequalities share common properties with usual logarithmic Sobolev inequalities, as tensorisation or perturbation, and imply as well Poincaré inequality. We also study the link between these new modified logarithmic Sobolev inequalities and transportation inequalities.

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