Journée transport optimal, équation de Monge-Ampère et applications

# Moment measures

## by Prof. Dario CORDERO-ERAUSQUIN (Université Paris 6)

Europe/Paris
Amphithéâtre Léon Motchane (IHES)

### Amphithéâtre Léon Motchane

#### IHES

Le Bois Marie 35, route de Chartres 91440 Bures-sur-Yvette
Description

To every convex function $\psi$ tending to infinity at infinity we can associate its moment measure, which is the image by the gradient of $\psi$ of the measure with density $e^{-\psi}$. We aim at characterizing all the measures that can be obtained as moment measure of some convex function. This will be done by studying a variational problem that is closely related to the one of optimal transportation theory. This variational problem can be studied using tools from the geometry of log-concave measures.

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