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arXiv · 2402.14647

On the Central Limit Theorem for the log-partition function of 2D directed polymers

Clément Cosco·Anna Donadini
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Abstract

The log-partition function $ \log W_N(\beta)$ 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 $\beta=\beta_N=\hat{\beta}\sqrt{\pi/\log N}$, $\hat{\beta}\in (0,1)$ (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.

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Clément Cosco, Anna Donadini. 2024-02-22. On the Central Limit Theorem for the log-partition function of 2D directed polymers. https://arxiv.org/abs/2402.14647

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