A Theory of Transfers: Duality and convolution

Understand

We introduce and study the permanence properties of the class of linear transfers between probability measures.

• This class contains all cost minimizing mass transports, but also martingale mass transports, the Schrodinger bridge associated to a reversible Markov process, and the weak mass transports of Tala- grand, Marton, Gozlan and others.
• The class also includes various stochastic mass transports to which Monge-Kantorovich theory does not apply.
• We also introduce the cone of convex transfers, which include any p-power (p > 1) of a linear transfer, but also the logarithmic entropy, the Donsker-Varadhan infor- mation and certain free energy functionals.