On the Lipschitz properties of transportation along heat flows
Probability
2025-11-25 v4 Analysis of PDEs
Functional Analysis
Abstract
We prove new Lipschitz properties for transport maps along heat flows, constructed by Kim and Milman. For (semi)-log-concave measures and Gaussian mixtures, our bounds have several applications: eigenvalues comparisons, dimensional functional inequalities, and domination of distribution functions.
Keywords
Cite
@article{arxiv.2201.01382,
title = {On the Lipschitz properties of transportation along heat flows},
author = {Dan Mikulincer and Yair Shenfeld},
journal= {arXiv preprint arXiv:2201.01382},
year = {2025}
}
Comments
Added smoothness assumption on density