On the Central Limit Theorem for the log-partition function of 2D directed polymers
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866908510754701312 |
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| author | Cosco, Clément Donadini, Anna |
| author_facet | Cosco, Clément Donadini, Anna |
| contents | The log-partition function $ \log W_N(β)$ of the two-dimensional directed polymer in random environment is known to converge in distribution to a normal distribution when considering temperature in the subcritical regime $β=β_N=\hatβ\sqrt{π/\log N}$, $\hatβ\in (0,1)$ (Caravenna, Sun, Zygouras, Ann. Appl. Prob. (2017)). In this paper, we present an elementary proof of this result relying on a decoupling argument and the central limit theorem for sums of independent random variables. The argument is inspired by an analogy of the model to branching random walks. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_14647 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the Central Limit Theorem for the log-partition function of 2D directed polymers Cosco, Clément Donadini, Anna Probability Primary: 60F05, Secondary: 82D60, 82B44, 60G50 The log-partition function $ \log W_N(β)$ of the two-dimensional directed polymer in random environment is known to converge in distribution to a normal distribution when considering temperature in the subcritical regime $β=β_N=\hatβ\sqrt{π/\log N}$, $\hatβ\in (0,1)$ (Caravenna, Sun, Zygouras, Ann. Appl. Prob. (2017)). In this paper, we present an elementary proof of this result relying on a decoupling argument and the central limit theorem for sums of independent random variables. The argument is inspired by an analogy of the model to branching random walks. |
| title | On the Central Limit Theorem for the log-partition function of 2D directed polymers |
| topic | Probability Primary: 60F05, Secondary: 82D60, 82B44, 60G50 |
| url | https://arxiv.org/abs/2402.14647 |