论文标题
对数Sobolev不平等的Feynman-KAC方法
A Feynman-Kac approach for Logarithmic Sobolev Inequalities
论文作者
论文摘要
本说明提出了一种基于对数Sobolev不平等的Feynman-Kac半群的方法。它遵循Bonnefont和Joulin在扩散操作员的交织关系方面的最新工作，该关系以前用于光谱间隙不平等，与扰动技术有关。特别是，它超越了贝克里 - {é}标准，并允许研究对最佳对数Sobolev常数的高维效应。我们最终与Holley-Strock方法进行了简短的比较。
This note presents a method based on Feynman-Kac semigroups for logarithmic Sobolev inequalities. It follows the recent work of Bonnefont and Joulin on intertwining relations for diffusion operators, formerly used for spectral gap inequalities, and related to perturbation techniques. In particular, it goes beyond the Bakry-{É}mery criterion and allows to investigate high-dimensional effects on the optimal logarithmic Sobolev constant.The method is illustrated on particular examples (namely Subbotin distributions and double-well potentials), for which explicit dimension-free bounds on the latter constant are provided. We eventually discuss a brief comparison with the Holley-Stroock approach.
