A lack of Ricci bounds for the entropic measure on Wasserstein space over the interval

作者：Chodosh Otis^*

来源：Journal of Functional Analysis, 2012, 262(10): 4570-4581.

DOI：10.1016/j.jfa.2012.03.007

• Wasserstein space
• Optimal transport
• Geometry of spaces of measures
• Lower bounds on curvature

We examine the entropic measure, recently constructed by von Renesse and Sturm, a measure over the metric space of probability measures on the unit interval equipped with the 2-Wasserstein distance. We show that equipped with this measure, Wasserstein space over the interval does not admit generalized Ricci lower bounds in the entropic displacement convexity sense of Lott-Villani-Sturm. We discuss why this is contrary to what one might expect from heuristic considerations.

• 出版日期2012-5-15