Poisson processes and a log-concave Bernstein theorem

Bo'az Klartag, Joseph Lehec

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish
Pages (from-to)85-107
Number of pages23
JournalStudia Mathematica
Volume247
Issue number1
DOIs
StatePublished - 2019

Keywords

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

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