A coupling of Brownian motions in the L0-geometry

Takafumi Amaba, Kazumasa Kuwada

Research output: Contribution to journalArticle

Abstract

Under a complete Ricci flow, we construct a coupling of two Brownian motions such that their L0-distance is a supermartingale. This recovers a result of Lott [J. Lott, Optimal transport and Perelman's reduced volume, Calc. Var. Partial Differential Equations 36(2009), no. 1,49-84.] on the monotonicity of L0-distance between heat distributions.

Original languageEnglish
Pages (from-to)139-174
Number of pages36
JournalTohoku Mathematical Journal
Volume70
Issue number1
Publication statusPublished - 2018 Mar

Keywords

  • Approximation by geodesic random walks
  • Coupling of brownian motions
  • Cq-gexxnetty

ASJC Scopus subject areas

  • Mathematics(all)

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  • Cite this

    Amaba, T., & Kuwada, K. (2018). A coupling of Brownian motions in the L0-geometry. Tohoku Mathematical Journal, 70(1), 139-174.