Rearrangement and Prékopa–Leindler Type Inequalities

  • James MelbourneEmail author
Conference paper
Part of the Progress in Probability book series (PRPR, volume 74)


We investigate the interactions of functional rearrangements with Prékopa–Leindler type inequalities. It is shown that certain set theoretic rearrangement inequalities can be lifted to functional analogs, thus demonstrating that several important integral inequalities tighten on functional rearrangement about “isoperimetric” sets with respect to a relevant measure. Applications to the Borell–Brascamp–Lieb, Borell–Ehrhard, and the recent polar Prékopa–Leindler inequalities are demonstrated. It is also proven that an integrated form of the Gaussian log-Sobolev inequality sharpens on rearrangement.


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Electrical and Computer EngineeringUniversity of MinnesotaMinneapolisUSA

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