Weak logarithmic Sobolev inequalities and entropic convergence
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, etc.). 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.
connection with various others functional inequalities (weak Poincaré inequalities, general
Beckner inequalities, etc.). 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.
Abstract
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, etc.). 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.
Springer
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