A coupling of Brownian motions in the $\mathcal{L}_0$-geometry
Probability
2014-08-04 v1 Differential Geometry
Abstract
Under a complete Ricci flow, we construct a coupling of two Brownian motion such that their -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 -distance between heat distributions.
Keywords
Cite
@article{arxiv.1408.0160,
title = {A coupling of Brownian motions in the $\mathcal{L}_0$-geometry},
author = {Takafumi Amaba and Kazumasa Kuwada},
journal= {arXiv preprint arXiv:1408.0160},
year = {2014}
}