Directed random walks on hierarchic trees with continuous branching: a renormalization group approach

We investigate the directed random walk on hierarchic trees. Two cases are investigated: random variables on deterministic trees with a continuous branching, and random variables on the trees constructed trough the random branching process. We derive renormalization group (partial differential) equations for the branching models with binomial, Poisson and compound Poisson distributions of random variables on the links of tree. These renormaliation group equations are new class of reaction-diffusion equations in 1-dimension.