Slowing down conditioned random walks to recover optimal transport on a graph
Christian Léonard (Univ. Paris Nanterre)
On a non-oriented metric graph, we build a convergent sequence of random walks with an asymptotically vanishing frequency of jumps. Its limit is a non-deterministic random walk which allows to solve the Monge-Kantorovich metric problem on the graph. Each random walk solves a Schroedinger problem, i.e. an entropic minimization problem of processes with prescribed
initial and final constraints.