Abstract
The universality of the directed polymer model and the analogous KPZ 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 \emph{finite size} estimates of the energy exponents are below the persumed universal values, these estimates \emph{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.
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