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Weak logarithmic Sobolev inequalities and entropic convergence.

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Date
2007-01
Link to item file
http://hal.archives-ouvertes.fr/hal-00013700/fr/
Dewey
Probabilités et mathématiques appliquées
Sujet
Probability
Journal issue
Probability Theory and Related Fields
Volume
139
Number
3-4
Publication date
2007
Article pages
563-603
Publisher
Springer
DOI
http://dx.doi.org/10.1007/s00440-007-0054-5
URI
https://basepub.dauphine.fr/handle/123456789/230
Collections
  • CEREMADE : Publications
Metadata
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Author
Cattiaux, Patrick
Gentil, Ivan
Guillin, Arnaud
Type
Article accepté pour publication ou publié
Abstract (EN)
In this paper we introduce and study a weakened form of logarithmic Sobolev inequalities in connection with various others functional inequalities (weak Poincaré inequalities, general Beckner inequalities...). We also discuss the quantitative behaviour of relative entropy along a symmetric diffusion semi-group. In particular, we exhibit an example where Poincaré inequality can not be used for deriving entropic convergence whence weak logarithmic Sobolev inequality ensures the result.

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