Some geometric consequences of the Schrödinger problem

Christian Léonard (1)

1 MODAL'X - Modélisation aléatoire de Paris X

This note presents a short review of the Schrödinger problem and of the first steps that might lead to interesting consequences in terms of geometry. We stress the analogies between this entropy minimization problem and the renowned optimal transport problem, in search for a theory of lower bounded curvature for metric spaces, including discrete graphs.

Mots clés: displacement interpolations; optimal transport; entropic interpolations; Lott-Sturm-Villani theory; lower bounded curvature of metric spaces; Schrödinger problem

Domaines: Probabilités [math.PR]

Christian Léonard. Some geometric consequences of the Schrödinger problem. Second International Conference on Geometric Science of Information, GSI 2015, 2015, Palaiseau, France. pp.60-68, ⟨10.1002/mana.201200324⟩. ⟨hal-01273094⟩