A SUM-OVER-PATHS APPROACH TO DIFFUSION ON TREES

We use a 'sum-over-paths' method to derive an explicit expression for the Green's function of the diffusion equation on an arbitrary tree, m aking connection with the conventional Laplace approach but emphasizin g the real-time nature of the technique. This provides a general frame work for studying both discrete-space and continuous-space diffusion p rocesses on complex one-dimensional topologies.