Abstract: Optimal transport has deep connections with Hamiltonian flows, Nelson’s stochastic mechanics and Mean field games. In this talk, we further study the Wasserstein probability manifold and its Hamiltonian flow on finite graphs. The Hamiltonian flow will be established as the second order ODE on the probability manifold. Several examples including Schrodinger equation, Schrodinger bridge problems will be discussed. Their relation to entropy production on finite graphs will be explained in Hamiltonian flows.
These are based on joint works with Wuchen Li (UCLA) and Haomin Zhou (GT).