Poisson processes and a log-concave Bernstein theorem
Probability
2018-07-10 v2 Functional Analysis
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.
Cite
@article{arxiv.1802.04176,
title = {Poisson processes and a log-concave Bernstein theorem},
author = {Bo'az Klartag and Joseph Lehec},
journal= {arXiv preprint arXiv:1802.04176},
year = {2018}
}