POINCARÉ AND LOGARITHMIC SOBOLEV INEQUALITIES FOR NEARLY RADIAL MEASURES

Abstract : If Poincaré inequality has been studied by Bobkov for radial measures, few is known about the logarithmic Sobolev inequalty in the radial case. We try to fill this gap here using different methods: Bobkov's argument and super-Poincaré inequalities, direct approach via L1-logarithmic Sobolev inequalities. We also give various examples where the obtained bounds are quite sharp. Recent bounds obtained by Lee-Vempala in the logconcave bounded case are refined for radial measures.
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https://hal.archives-ouvertes.fr/hal-02418658
Contributor : Arnaud Guillin <>
Submitted on : Thursday, December 19, 2019 - 9:02:43 AM
Last modification on : Friday, January 10, 2020 - 9:09:02 PM

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  • HAL Id : hal-02418658, version 1
  • ARXIV : 1912.10825

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Patrick Cattiaux, Arnaud Guillin, Liming Wu. POINCARÉ AND LOGARITHMIC SOBOLEV INEQUALITIES FOR NEARLY RADIAL MEASURES. 2019. ⟨hal-02418658⟩

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