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 publiéExternal document link
http://hal.archives-ouvertes.fr/hal-00013700/fr/Date
2007-01Journal name
Probability Theory and Related FieldsVolume
139Number
3-4Publisher
Springer
Pages
563-603
Publication identifier
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Show full item recordAbstract (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
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