Universality of the directed polymer model

The universality of the directed polymer model and the analogous Kardar-Parisi-Zhang equation is supported by numerical simulations using non-Gaussian random probability distributions in two, three, and four dimensions. It is shown that although in the non-Gaussian cases the finite size estimates of the energy exponents are below the presumed universal values, these estimates increase with the system size, and the further they are below the universal values, the higher is their rate of increase. The results are explained in terms of the efficiency of variance reduction during the optimization process.