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

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Abstract 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… Click to show full abstract

Abstract 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: quantitative forms; transport inequalities; concave measures; inequalities log; log concave

Journal Title: Canadian Journal of Mathematics
Year Published: 2017

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