DIRECTED POLYMERS ON TREES - A MARTINGALE APPROACH

We use martingale methods and simple convexity arguments to compute rigorously the limiting free energy in the problem of directed polymers on a tree. The limit is a degenerate random variable and convergence holds almost surely. The only assumption on the common distribution of the random potentials attached to the bonds of the tree is that its Laplace transform exists everywhere in [0, infinity).