Rearrangement and Prekopa-Leindler type inequalities
Probability
2019-05-24 v2 Information Theory
Functional Analysis
math.IT
Abstract
We investigate the interactions of functional rearrangements with Prekopa-Leindler type inequalities. It is shown that that a general class of integral inequalities tighten on rearrangement to "isoperimetric" sets with respect to a relevant measure. Applications to the Borell-Brascamp-Lieb, Borell-Ehrhart, and the recent polar Prekopa-Leindler inequalities are demonstrated. It is also proven that an integrated form of the Gaussian log-Sobolev inequality decreases on half-space rearrangement.
Keywords
Cite
@article{arxiv.1806.08837,
title = {Rearrangement and Prekopa-Leindler type inequalities},
author = {James Melbourne},
journal= {arXiv preprint arXiv:1806.08837},
year = {2019}
}
Comments
22 pages