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

arXiv: Probability, 2019.

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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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