Globally Lipschitz Transport Maps

par Max Fathi (LJLL & LPSM)

vendredi 13 oct. 2023, 14:00 → 16:00 Europe/Paris

Amphithéâtre Léon Motchane (IHES)

Probability and analysis informal seminar

One way of proving probabilistic functional inequalities (concentration inequalities, logarithmic Sobolev inequalities...) is to use a change of variables, to transfer them from a simple reference measure (typically, Gaussian) to more general settings. One example of this is the Caffarelli contraction theorem, which states that uniformly log-concave measures can be realized as images of standard Gaussian measures by globally lipschitz maps, using the L2 optimal transport map. One open problem in this direction is to find an analogue of Caffarelli's theorem in the Riemannian setting.

In this talk, I will present a stochastic construction of non-optimal maps, due to Kim and Milman, and Lipschitz estimates in various settings, including certain measures on Riemannian manifolds. Joint work with Dan Mikulincer and Yair Shenfeld. 

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