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.
- Approximation by geodesic random walks
- Coupling of brownian motions
ASJC Scopus subject areas