A COUPLING OF BROWNIAN MOTIONS IN THE L0-GEOMETRY

被引：0
|
作者：
Amaba, Takafumi [1 ]
Kuwada, Kazumasa [2 ]
机构：
[1] Fukuoka Univ, Fac Sci, Dept Appl Math, Fukuoka 8130180, Japan
[2] Tohoku Univ, Math Inst, Sendai, Miyagi 9808578, Japan
来源：
TOHOKU MATHEMATICAL JOURNAL | 2018年 / 70卷 / 01期
关键词：
L-0-geometry; coupling of Brownian motions; approximation by geodesic random walks; RICCI FLOW; OPTIMAL TRANSPORTATION; MANIFOLDS; CURVATURE; ENTROPY; TIME;
D O I：
10.2748/tmj/1520564422
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Under a complete Ricci flow, we construct a coupling of two Brownian motions such that their L-0-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 L-0-distance between heat distributions.
引用
收藏
页码：139 / 174
页数：36
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