TRANSPORT PROOFS OF SOME DISCRETE VARIANTS OF THE PRÉKOPA-LEINDLER INEQUALITY

Abstract : We give a transport proof of a discrete version of the displacement convexity of entropy on integers (Z), and get, as a consequence, two discrete forms of the Prékopa-Leindler Inequality : the Four Functions Theorem of Ahlswede and Daykin on the discrete hypercube [1] and a recent result on Z due to Klartag and Lehec [16].
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https://hal.archives-ouvertes.fr/hal-02123268
Contributor : Paul-Marie Samson <>
Submitted on : Tuesday, May 7, 2019 - 10:10:41 PM
Last modification on : Sunday, May 12, 2019 - 1:14:25 AM

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  • HAL Id : hal-02123268, version 1
  • ARXIV : 1905.04038

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Nathael Gozlan, Cyril Roberto, Paul-Marie Samson, Prasad Tetali. TRANSPORT PROOFS OF SOME DISCRETE VARIANTS OF THE PRÉKOPA-LEINDLER INEQUALITY. 2019. ⟨hal-02123268⟩

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