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Article Dans Une Revue Annali della Scuola Normale Superiore di Pisa Année : 2021

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

Résumé

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].

Dates et versions

hal-03825123 , version 1 (21-10-2022)

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Nathael Gozlan, Cyril Roberto, Paul-Marie Samson, Prasad Tetali. Transport Proofs Of Some Discrete Variants Of The Pr{\'e}Kopa-leindler Inequality. Annali della Scuola Normale Superiore di Pisa, 2021. ⟨hal-03825123⟩
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