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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Accesso online: | https://arxiv.org/abs/2509.21453 |
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| _version_ | 1866916970704666624 |
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| author | Agarwal, Pranay |
| author_facet | Agarwal, Pranay |
| contents | 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 arXiv:2304.04871, 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 $α\in (2/(3K+11), 1/4)$, 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_21453 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Improved universality bounds for directed polymers in the intermediate disorder regime Agarwal, Pranay Probability 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 arXiv:2304.04871, 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 $α\in (2/(3K+11), 1/4)$, 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. |
| title | Improved universality bounds for directed polymers in the intermediate disorder regime |
| topic | Probability |
| url | https://arxiv.org/abs/2509.21453 |