Modified logarithmic Sobolev inequalities in null curvature
Ivan Gentil
Université Claude Bernard Lyon 1, Villeurbanne, FranceArnaud Guillin
Université de Provence, Marseille, FranceLaurent Miclo
Université de Provence, Marseille, France
![Modified logarithmic Sobolev inequalities in null curvature cover](/_next/image?url=https%3A%2F%2Fcontent.ems.press%2Fassets%2Fpublic%2Fimages%2Fserial-issues%2Fcover-rmi-volume-23-issue-1.png&w=3840&q=90)
Abstract
We present a new logarithmic Sobolev inequality adapted to a log-concave measure on between the exponential and the Gaussian measure. More precisely, assume that is a symmetric convex function on satisfying for large enough and with . We prove that the probability measure on satisfies a modified and adapted logarithmic Sobolev inequality: there exist three constants such that for all smooth functions ,
with
where is the Legendre–Fenchel transform of .
Cite this article
Ivan Gentil, Arnaud Guillin, Laurent Miclo, Modified logarithmic Sobolev inequalities in null curvature. Rev. Mat. Iberoam. 23 (2007), no. 1, pp. 235–258
DOI 10.4171/RMI/493