Search

Talk

Lipschitz transport maps via heat flow

  • Max Fathi (Université de Paris, LJLL & LPSM)
E1 05 (Leibniz-Saal)

Abstract

Globally lipschitz transport maps have found many applications in the study of probabilistic functional inequalities such as logarithmic Sobolev and Poincaré inequalities, by transporting an inequality from a nice reference measure to another one. For example, a theorem of Caffarelli states that optimal transport maps from the standard Gaussian measure onto uniformly log-concave measures are $1$-lipschitz. This then recovers the sharp bounds of Bakry and Emery on the logarithmic Sobolev constant of such measures.

In this talk, I will discuss a construction of non-optimal transport maps using the heat flow, due to Kim and Milman, and explain how it allows to get dimension-free lipschitz maps in new settings, including certain Riemannian manifolds. Joint work with D. Mikulincer and Y. Shenfeld.

Upcoming Events of this Seminar

  • Dienstag, 11.03.25 tba with Jianfeng Lu
  • Dienstag, 11.03.25 tba with Steffen Börm
  • Dienstag, 06.05.25 tba with Ilya Chevyrev
  • Dienstag, 03.06.25 tba with Mate Gerencser