I will present some results from the paper "The L1 contraction principle in optimal transport" by M. Jacobs, I. Kim and J. Tong, which lead to a proof of the discrete contraction principle at the level of the JKO scheme. We will consider local energy functionals given by non-spatially homogeneous convex functions and general cost functions via the equivalent dual problem which is easier to treat. I will show how the interplay between the primal and dual problem easily allows us to derive the contraction principle, and present some applications and consequences as time permits.
