Poisson processes and a log-concave Bernstein theorem

Bo'az Klartag, Joseph Lehec

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)85-107
Number of pages23
JournalStudia Mathematica
Issue number1
StatePublished - 2019


FundersFunder number
European Research Council


    • Laplace transform
    • Log-concave measures
    • Log-concave sequences
    • Poisson processes


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