Transport Proofs Of Some Discrete Variants Of The PréKopa-leindler Inequality

2019/05/10 by Nathaël Gozlan, Cyril Roberto, Gozlan, Nathael +5 · 3 citations
Mathematics · #FOS: Mathematics #Functional Analysis (math.FA) #Geometric Analysis and Curvature Flows #Mathematical Dynamics and Fractals #Probability (math.PR) #Spectral Theory in Mathematical Physics

paper · doi:10.48550/arxiv.1905.04038

openalex publication_date 2019/05/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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].

Cited by

• The stability of log-supermodularity under convolution
• From Brunn-Minkowski to Prékopa-Leindler and Borell-Brascamp-Lieb: discrete inequalities
• Functional Liftings of Restricted Geometric Inequalities

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