Séminaire de Averil Aussedat (Université de Pise, Italie)
Séminaire de Modélisation et d’Analyse appliquée
Jeudi 11/12/2025, 14H30, Salle M003
Titre : Decomposition of a measure according to Wasserstein tangent cones
Résumé : A probability measure can be transported to another measure through the optimal transport plans achieving the Wasserstein distance. These plans might be deterministic or split mass : we show that the first measure can be decomposed in d+1 parts, each allowing (martingale) optimal plans to split mass in a fixed number of directions, from 0 to d. In addition, the directions of splitting are orthogonal to some sets over which the measure is concentrated, each being covered by c-c hypersurfaces of a fixed dimension.
