Improved universality bounds for directed polymers in the intermediate disorder regime

We prove universality of Tracy–Widom GUE fluctuations for directed polymers in 1+1 dimensions in the intermediate disorder regime. Building on the Lindeberg replacement method of [Ran25], we refine estimates for the measure of steep paths using probabilistic arguments. Our result extends the admissible range of the inverse temperature scaling parameter β=n−α to all α∈(2∕(3K+11),1∕4), provided the weights match K moments with the log–Gamma distribution. For a general class of distributions, this gives universality for α>2∕17, and when the third moment vanishes, this threshold improves to α>1∕10. These results substantially broaden the known range of universality for directed polymers in the intermediate disorder regime.