The talk is based on a joint paper with T.Alberts and J.Quastel. We consider directed polymers in a random environment. However the inverse temperature is scaled with the length of a polymer. It turn out that with a proper critical scaling one can get a nontrivial universal behaviour for the partition function and the end point distribution. Moreover the limiting partition function distribution asymptotically converges to the Tracy-Widom law as the rescaled inverse temperature tends to infinity.

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Last updated: 06 Mar 2020