Poisson processes and a log-concave Bernstein theorem

Boaz Klartag , Joseph Lehec (1, 2)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
2 DMA - Département de Mathématiques et Applications - ENS Paris

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.

Domaines: Probabilités [math.PR]; Analyse fonctionnelle [math.FA]

Boaz Klartag, Joseph Lehec. Poisson processes and a log-concave Bernstein theorem. Studia Mathematica, 2019, 1 (247), pp.85-107. ⟨10.4064/sm180212-30-7⟩. ⟨hal-01708514⟩