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arXiv · 1905.04038

Transport Proofs Of Some Discrete Variants Of The Pr{\'e}Kopa-leindler Inequality

Nathael Gozlan·Cyril Roberto·Paul-Marie Samson·Prasad Tetali
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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 Pr{\'e}kopa-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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Nathael Gozlan, Cyril Roberto, Paul-Marie Samson, Prasad Tetali. 2019-05-10. Transport Proofs Of Some Discrete Variants Of The Pr{\'e}Kopa-leindler Inequality. https://arxiv.org/abs/1905.04038

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