Remarks on multi-marginals entropic optimal transport and Sinkhorn algorithm

Entropic optimal transport has received a lot of attention in recent years and has become a popular framework for computational optimal transport thanks to the Sinkhorn scaling algorithm. In this talk, I will discuss the multi-marginal case which arises in different applied contexts in physics, economics and machine learning. I will show in particular that the multi-marginal Schrödinger system is well posed (joint work with Maxime Laborde) and that the multi-marginal Sinkhorn algorithm converges linearly.