A Feynman-Kac approach for logarithmic Sobolev inequalities

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. In particular, it goes beyond the Bakry-{E}mery criterion and allows to investigate high-dimensional effects on the optimal logarithmic Sobolev constant. The method is finally illustrated on particular examples, for which explicit dimension-free bounds on the latter constant are provided.