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

Preuve par transport de mesure de versions discrètes de l'inégalité de Preekopa-Leindler

Nathael Gozlan (1) , Cyril Roberto (2, 3) , Paul-Marie Samson (4) , Prasad Tetali (5)

1 MAP5 - UMR 8145 - Mathématiques Appliquées Paris 5
2 MODAL'X - Modélisation aléatoire de Paris X
3 FP2M - Fédération Parisienne de Modélisation Mathématique
4 LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées
5 School of Mathematics - School of Mathematics, School of Computer Science

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].

Domaines: Probabilités [math.PR]; Analyse fonctionnelle [math.FA]

Nathael Gozlan, Cyril Roberto, Paul-Marie Samson, Prasad Tetali. TRANSPORT PROOFS OF SOME DISCRETE VARIANTS OF THE PRÉKOPA-LEINDLER INEQUALITY. Annali della Scuola Normale Superiore di Pisa, Classe di Scienze, 2021, pp.1207-1232. ⟨10.2422/2036-2145.201906_002⟩. ⟨hal-02123268⟩