Lipschitz transport maps via heat flow

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


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.

Katja Heid

MPI for Mathematics in the Sciences Contact via Mail

Upcoming Events of This Seminar

  • Mar 12, 2024 tba with Theresa Simon
  • Mar 26, 2024 tba with Phan Thành Nam
  • Mar 26, 2024 tba with Dominik Schmid
  • May 7, 2024 tba with Manuel Gnann
  • May 14, 2024 tba with Barbara Verfürth
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  • Jun 25, 2024 tba with Paul Dario
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