Some remarks on weighted logarithmic Sobolev inequality

  title={Some remarks on weighted logarithmic Sobolev inequality},
  author={Patrick Cattiaux and Arnaud Guillin and Liming Wu},
  journal={arXiv: Probability},
We give here a simple proof of weighted logarithmic Sobolev inequality, for example for Cauchy type measures, with optimal weight, sharpening results of Bobkov-Ledoux. Some consequences are also discussed. 

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