High moments of 2d directed polymers up to quasi-criticality
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866910888532901888 |
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| author | Cosco, Clément Nakajima, Shuta |
| author_facet | Cosco, Clément Nakajima, Shuta |
| contents | We consider two-dimensional directed polymers in random environment in the sub-critical regime and in the quasi-critical regime introduced recently by Caravenna, Cottini and Rossi, arXiv:2307.02453v1. For $q\leq q_N$ with $q_N\to\infty$ diverging at a suitable rate with the size of the system, we obtain upper bound estimates on the $q$-moment of the partition function for general environments. In the sub-critical regime, our results improve the $q_N$-threshold obtained for Gaussian environment in Cosco, Zeitouni, Comm. Math. Phys (2023). As a corollary, we derive large deviation estimates with a Gaussian rate function. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2503_17232 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | High moments of 2d directed polymers up to quasi-criticality Cosco, Clément Nakajima, Shuta Probability Primary 60K37, secondary 60K35, 82C44, 82D30 We consider two-dimensional directed polymers in random environment in the sub-critical regime and in the quasi-critical regime introduced recently by Caravenna, Cottini and Rossi, arXiv:2307.02453v1. For $q\leq q_N$ with $q_N\to\infty$ diverging at a suitable rate with the size of the system, we obtain upper bound estimates on the $q$-moment of the partition function for general environments. In the sub-critical regime, our results improve the $q_N$-threshold obtained for Gaussian environment in Cosco, Zeitouni, Comm. Math. Phys (2023). As a corollary, we derive large deviation estimates with a Gaussian rate function. |
| title | High moments of 2d directed polymers up to quasi-criticality |
| topic | Probability Primary 60K37, secondary 60K35, 82C44, 82D30 |
| url | https://arxiv.org/abs/2503.17232 |