Recently, Bauke and Mertens conjectured that the local statistics of energies in random spin systems with discrete spin space should, in most circumstances, be the same as in the random energy model. We show that this conjecture holds true as well for directed polymers in random environment. We also show that, under certain conditions, this conjecture holds for directed polymers even if energy levels that grow moderately with the volume of the system are considered.
Irina Kurkova. "Local Energy Statistics in Directed Polymers." Electron. J. Probab. 13 5 - 25, 2008. https://doi.org/10.1214/EJP.v13-475