Weak logarithmic Sobolev inequalities and entropic convergence

Details Weak logarithmic Sobolev inequalities and entropic convergence Weak logarithmic Sobolev inequalities and entropic convergence

2005-11-10

arxiv.org/abs/math/0511255v2

Mathematics

Probability

Scientific paper

In this paper we introduce and study a weakened form of logarithmic Sobolev inequalities in connection with various others functional inequalities (weak Poincar\'{e} 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 Poincar\'{e} inequality can not be used for deriving entropic convergence whence weak logarithmic Sobolev inequality ensures the result.

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