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

详细信息	查看全文 | 推荐本文 |

• 作者：Otis Chodosh ^{ochodosh@math.stanford.edu}
• 关键词：Wasserstein space ; Optimal transport ; Geometry of spaces of measures ; Lower bounds on curvature
• 刊名：Journal of Functional Analysis
• 出版年：2012
• 期刊代码：75_00221236
• 类别：mt
• 出版时间：15 May, 2012
• 卷：262
• 期：10
• 页码：4570-4581
• 文件大小：143 K

摘要

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.