Lipschitz Transport Maps via the Follmer Flow
Probability
2023-09-08 v1
Abstract
Inspired by the construction of the F{\"o}llmer process, we construct a unit-time flow on the Euclidean space, termed the F{\"o}llmer flow, whose flow map at time 1 pushes forward a standard Gaussian measure onto a general target measure. We study the well-posedness of the F{\"o}llmer flow and establish the Lipschitz property of the flow map at time 1. We apply the Lipschitz mapping to several rich classes of probability measures on deriving dimension-free functional inequalities and concentration inequalities for the empirical measure.
Keywords
Cite
@article{arxiv.2309.03490,
title = {Lipschitz Transport Maps via the Follmer Flow},
author = {Yin Dai and Yuan Gao and Jian Huang and Yuling Jiao and Lican Kang and Jin Liu},
journal= {arXiv preprint arXiv:2309.03490},
year = {2023}
}