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Transport Inequalities for Log-concave Measures, Quantitative Forms, and Applications

Published online by Cambridge University Press:  20 November 2018

Dario Cordero-Erausquin
Dario Cordero-Erausquin*
Affiliation:
Institut de Mathématiques de Jussieu, Université Pierre et Marie Curie -Paris 6, 75252 Paris Cedex 05, France e-mail: dario.cordero@imj-prg.fr
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Abstract

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We review some simple techniques based on monotone-mass transport that allow us to obtain transport-type inequalities for any log-concave probability measures, and for more general measures as well. We discuss quantitative forms of these inequalities, with application to the Brascamp–Lieb variance inequality.

Keywords

52A4060E1549Q20log-concave measurestransport inequalityBrascamp-Lieb inequalityquantitative inequalities
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 69 , Issue 3 , 01 June 2017 , pp. 481 - 501
Copyright
Copyright © Canadian Mathematical Society 2017

References

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