Events

Stability of optimal transport: old and new

Speaker: Cyril Letrouit

Location: 60 Fifth Avenue, Room Auditorium Hall 150

Date: Thursday, September 19, 2024

Optimal transport consists in sending a given source probability measure to a given target probability measure, in a way which is optimal with respect to some cost. On bounded subsets of R^d, if the cost is given by the squared Euclidean distance and the source measure is absolutely continuous, a unique optimal transport map exists.

The question we will discuss is the following: how does this optimal transport map change if we perturb the target measure? For instance, if instead of the target measure we only have access to samples of it, how much does the optimal transport map change? This question, motivated by numerical aspects of optimal transport, has started to receive partial answers only recently, under quite restrictive assumptions on the source measure. We will review these answers and show how to handle much more general cases.

This is a joint work with Quentin Mérigot.