Poisson processes and a log-concave Bernstein theorem

Bo'az Klartag; Joseph Lehec

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arXiv · 1802.04176

Poisson processes and a log-concave Bernstein theorem

Bo'az Klartag·Joseph Lehec

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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 Pr\'ekopa-Leindler and the Walkup theorems. One of our main tools is a stochastic variational formula for the Poisson average.

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Bo'az Klartag, Joseph Lehec. 2018-02-12. Poisson processes and a log-concave Bernstein theorem. https://arxiv.org/abs/1802.04176

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