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For a directed polymer model in random environment, a characterization of theweak disorder phase in terms of the moment of the renormalized partitionfunction has been proved in [S. Junk: Communications in Mathematical Physics389, 1087-1097 (2022)]. We extend this characterization to a large class ofunbounded environments which includes many commonly used distributions.

Moment characterization of the weak disorder phase for directed polymers in a class of unbounded environments