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

Otis Chodosh

Research output: Contribution to journalArticle

3 Scopus citations

Abstract

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.

Original languageEnglish (US)
Pages (from-to)4570-4581
Number of pages12
JournalJournal of Functional Analysis
Volume262
Issue number10
DOIs
StatePublished - May 15 2012

All Science Journal Classification (ASJC) codes

  • Analysis

Keywords

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

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