ON A MIXTURE OF BRENIER AND STRASSEN THEOREMS

Nathael Gozlan (1) , Nicolas Juillet (2)

1 MAP5 - UMR 8145 - Mathématiques Appliquées Paris 5
2 IRMA - Institut de Recherche Mathématique Avancée

We give a characterization of optimal transport plans for a variant of the usual quadratic transport cost introduced in [33]. Optimal plans are composition of a deterministic transport given by the gradient of a continuously differentiable convex function followed by a martingale coupling. We also establish some connections with Caffarelli’s contraction theorem [14].

Mots clés: Optimal transport; Martingales; Brenier Theorem; Strassen Theorem

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

Nathael Gozlan, Nicolas Juillet. ON A MIXTURE OF BRENIER AND STRASSEN THEOREMS. Proceedings of the London Mathematical Society, 2020, ⟨10.1112/plms.12302⟩. ⟨hal-01855463v2⟩