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Poisson processes and a log-concave Bernstein theorem

Klartag, Bo'az; Lehec, Joseph (2019), Poisson processes and a log-concave Bernstein theorem, Studia Mathematica, 247, p. 85-107. 10.4064/sm180212-30-7

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Article accepté pour publication ou publié
External document link
https://hal.archives-ouvertes.fr/hal-01708514
Date
2019
Journal name
Studia Mathematica
Number
247
Publisher
Instytut Matematyczny- Polska Akademia Nauk
Pages
85-107
Publication identifier
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Author(s)
Klartag, Bo'az
Weizmann Institute of Science
Lehec, Joseph cc
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Département de Mathématiques et Applications - ENS Paris [DMA]
Abstract (EN)
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.
Subjects / Keywords
log-concave functions; log-concave sequences