Quasi-critical fluctuations for 2d directed polymers
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866916725185839104 |
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| author | Caravenna, Francesco Cottini, Francesca Rossi, Maurizia |
| author_facet | Caravenna, Francesco Cottini, Francesca Rossi, Maurizia |
| contents | We study the 2d directed polymer in random environment in a novel *quasi-critical regime*, which interpolates between the much studied sub-critical and critical regimes. We prove Edwards-Wilkinson fluctuations throughout the quasi-critical regime, showing that the diffusively rescaled partition functions are asymptotically Gaussian. We deduce a corresponding result for the critical 2d Stochastic Heat Flow. A key challenge is the lack of hypercontractivity, which we overcome deriving new moment estimates. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_02453 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Quasi-critical fluctuations for 2d directed polymers Caravenna, Francesco Cottini, Francesca Rossi, Maurizia Probability Mathematical Physics Primary: 82B44, Secondary: 60F05, 35R60 We study the 2d directed polymer in random environment in a novel *quasi-critical regime*, which interpolates between the much studied sub-critical and critical regimes. We prove Edwards-Wilkinson fluctuations throughout the quasi-critical regime, showing that the diffusively rescaled partition functions are asymptotically Gaussian. We deduce a corresponding result for the critical 2d Stochastic Heat Flow. A key challenge is the lack of hypercontractivity, which we overcome deriving new moment estimates. |
| title | Quasi-critical fluctuations for 2d directed polymers |
| topic | Probability Mathematical Physics Primary: 82B44, Secondary: 60F05, 35R60 |
| url | https://arxiv.org/abs/2307.02453 |