Weak logarithmic Sobolev inequalities and entropic convergence.

Cattiaux, Patrick; Gentil, Ivan; Guillin, Arnaud

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

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