A Lack of Ricci Bounds for the Entropic Measure on Wasserstein space over the Interval

Abstract

This is a condensed form of the author's essay, which can be found at [arXiv:1105.2883]. We prove that the entropic measure constructed by von Renesse-Sturm over Wasserstein space on the unit interval (probability measures on the unit interval equipped with the 2-Wasserstein metric) does not admit generalized Ricci lower bounds in the sense of Lott-Villani-Sturm. We discuss why this is surprising, considering various heuristic arguments.

References in corpus (2)

• Optimal Transport and Ricci Curvature: Wasserstein Space Over the Interval
• Entropic Measure on Multidimensional Spaces

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• A Rademacher-type Theorem on $L^2$-Wasserstein Spaces over Closed Riemannian Manifolds
• Dean-Kawasaki Dynamics: Ill-posedness vs. Triviality