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Aymeric Baradat

Lundi 26 novembre 2018

Aymeric Baradat (ENS)

Entropic regularization of incompressible optimal transport.

Résumé : I will present an elementary way to modify an absolutely continuous curve with values in the Wasserstein space to get an admissible curve for the dynamical entropic optimal transport. This construction allows to recover in a variational way two famous theorems :
- the displacement convexity of the entropy along the optimal transport (due to McCann),
- the Gamma-convergence of the dynamical entropic optimal transport towards the classical optimal transport (due to Léonard).
Besides, these proofs adapt transparently to the multiphasic incompressible case, so that we get as new results these theorems in that setting. Doing so, we extend a result by Lavenant for the convexity of the entropy, and a result by Benamou-Carlier-Nenna for the Gamma-convergence.

This is a joint work with L. Monsaingeon (Lisbon and Nancy University).