Abstract: The scaling behavior of the excited energy states of the directed polymer in random media is analyzed numerically. We find that the spatial correlations of polymer energies scale as -k- for small enough wave numbers k with a nontrivial exponent X=1.3. The equivalence between the stochastic-field equation that describes the partition function of the directed polymer and that governing the time evolution of infinitesimal perturbations in space-time chaos is exploited to connect this exponent d with the spatial correlations of the Lyapunov vectors reported in the literature. The relevance of our results for other problems involving optimization in random systems is discussed.

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