Poisson processes and a log-concave Bernstein theorem

2018/02/12 by Klartag, Bo'az, Lehec, Joseph · 3 citations
#FOS: Mathematics #Functional Analysis (math.FA) #Probability (math.PR)

paper · doi:10.48550/arxiv.1802.04176

Abstract

We discuss interplays between log-concave functions and log-concave sequences. We prove a Bernstein-type theorem, which characterizes the Laplace transform of log-concave measures on the half-line in terms of log-concavity of the alternating Taylor coefficients. We establish concavity inequalities for sequences inspired by the Prékopa-Leindler and the Walkup theorems. One of our main tools is a stochastic variational formula for the Poisson average.

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• 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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