Large deviations for the log-Gamma polymer
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866910664911486976 |
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| author | Claeys, Tom Mauersberger, Julian |
| author_facet | Claeys, Tom Mauersberger, Julian |
| contents | We conjecture an explicit expression for the lower tail large deviation rate function of the partition function of the log-Gamma polymer. We rigorously prove our result, except for one step for which we only provide heuristic evidence. We show that the large deviation rate function matches with that of last passage percolation with exponential weights in the zero-temperature limit, and with the lower tail of the Tracy-Widom distribution for moderate deviations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_18818 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Large deviations for the log-Gamma polymer Claeys, Tom Mauersberger, Julian Mathematical Physics Classical Analysis and ODEs Probability 82D60, 60B20, 60G55 We conjecture an explicit expression for the lower tail large deviation rate function of the partition function of the log-Gamma polymer. We rigorously prove our result, except for one step for which we only provide heuristic evidence. We show that the large deviation rate function matches with that of last passage percolation with exponential weights in the zero-temperature limit, and with the lower tail of the Tracy-Widom distribution for moderate deviations. |
| title | Large deviations for the log-Gamma polymer |
| topic | Mathematical Physics Classical Analysis and ODEs Probability 82D60, 60B20, 60G55 |
| url | https://arxiv.org/abs/2410.18818 |