Coupling of Brownian motions and Perelman's L-functional

Details Coupling of Brownian motions and Perelman's L-functional Coupling of Brownian motions and Perelman's L-functional

2010-07-08

arxiv.org/abs/1007.1400v1

Mathematics

Probability

20 pages

Scientific paper

We show that on a manifold whose Riemannian metric evolves under backwards Ricci flow two Brownian motions can be coupled in such a way that the expectation of their normalized L-distance is non-increasing. As an immediate corollary we obtain a new proof of a recent result of Topping (J. reine angew. Math. 636 (2009), 93-122), namely that the normalized L-transportation cost between two solutions of the heat equation is non-increasing as well.

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