Geodesic
Transport Inequalities for Log-concave Measures, Quantitative Forms, and Applications
Canadian journal of mathematics, Tome 69 (2017) no. 3, pp. 481-501

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DOI

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.
DOI : 10.4153/CJM-2016-046-3
Mots-clés : 52A40, 60E15, 49Q20, log-concave measures, transport inequality, Brascamp-Lieb inequality, quantitative inequalities 
Cordero-Erausquin, Dario. Transport Inequalities for Log-concave Measures, Quantitative Forms, and Applications. Canadian journal of mathematics, Tome 69 (2017) no. 3, pp. 481-501. doi: 10.4153/CJM-2016-046-3
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     title = {Transport {Inequalities} for {Log-concave} {Measures,} {Quantitative} {Forms,} and {Applications}},
     journal = {Canadian journal of mathematics},
     pages = {481--501},
     year = {2017},
     volume = {69},
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     doi = {10.4153/CJM-2016-046-3},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-2016-046-3/}
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