The central limit theorem for directed polymers in weak disorder, revisited

Stefan Junk

Published 2021-05-10Version 1

We give a new proof for the central limit theorem in probability for the directed polymer model in a bounded environment with bond disorder in the interior of the weak disorder phase. In the same setup, we also show that the large deviation rate function agrees with that of the underlying random walk. In addition, for the Brownian polymer model, we show that the central limit theorem holds almost surely in the whole weak disorder phase. The results are proved using the moment bound from [20] and a new tool introduced in this paper, which allows a quantitative comparison between the associated martingales at different inverse temperatures. This comparison is made precise using the noise operator $T_\rho$ acting on the environment by independent resampling.