Title:  Quantitative Uniform Stability of the Iterative Proportional Fitting Procedure.

Abstract: We establish the uniform in time stability, w.r.t. the marginals, of the Iterative Proportional Fitting Procedure, also known as Sinkhorn algorithm, used to solve entropy-regularised Optimal Transport problems. Our result is quantitative and stated in terms of the 1- Wasserstein metric. As a corollary we establish a quantitative stability result for Schrödinger bridges. This is joint work with V. de Bortoli and A. Doucet.