On the Lipschitz properties of transportation along heat flows
Massachusetts Institute of Technology（麻省理工学院）
Dan Mikulincer, Yair Shenfeld
备注：
Erroneous dimensional log-Sobolev inequality results removed. Bounds in Theorem 1 and Theorem 2 improved, and optimality of Theorem 2 about Gaussian mixtures established. Discussion on relation to Brownian transport map removed
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.
Université Paris Cité and Sorbonne Université, CNRS, Laboratoire Jacques Louis Lions & Laboratoire de Probabilités Statistique et Modélisation（巴黎西岱大学与索邦大学，法国国家科学研究中心，雅克-路易·利翁斯实验室与概率统计与建模实验室）；Institut Universitaire de France (IUF)（法国高等研究院）；Department of Mathematics, Massachusetts Institute of Technology（麻省理工学院数学系）；Division of Applied Mathematics, Brown University（布朗大学应用数学部）
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