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Weak logarithmic Sobolev inequalities and entropic convergence.

Cattiaux, Patrick; Gentil, Ivan; Guillin, Arnaud (2007), Weak logarithmic Sobolev inequalities and entropic convergence., Probability Theory and Related Fields, 139, 3-4, p. 563-603. http://dx.doi.org/10.1007/s00440-007-0054-5

Type
Article accepté pour publication ou publié
External document link
http://hal.archives-ouvertes.fr/hal-00013700/fr/
Date
2007-01
Journal name
Probability Theory and Related Fields
Volume
139
Number
3-4
Publisher
Springer
Pages
563-603
Publication identifier
http://dx.doi.org/10.1007/s00440-007-0054-5
Metadata
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Author(s)
Cattiaux, Patrick
Gentil, Ivan
Guillin, Arnaud
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.
Subjects / Keywords
Probability

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