On the Central Limit Theorem for the log-partition function of 2D directed polymers - Archive ouverte HAL
Pré-Publication, Document De Travail Année : 2024

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

Résumé

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.

Dates et versions

hal-04579481 , version 1 (17-05-2024)

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Citer

Clément Cosco, Anna Donadini. On the Central Limit Theorem for the log-partition function of 2D directed polymers. 2024. ⟨hal-04579481⟩
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