We give sharp estimate for the free energy of directed polymers in random environment in dimension 1+1. This estimate was known for a Gaussian environment, we extend it to the case where the law of the environment is infinitely divisible.
"Sharp asymptotics for the free energy of 1+1 dimensional directed polymers in an infinitely divisible environment." Electron. Commun. Probab. 17 1 - 9, 2012. https://doi.org/10.1214/ECP.v17-2221