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On the Central Limit Theorem for the log-partition function of 2D directed polymers
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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.
Forward citations
Cited by 2 Pith papers
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Fractional moments of the Stochastic Heat Flow and 2D Directed Polymers
For 0<p<1, the p-th moment of the critical 2D SHF mass on a small ball is bounded by the second moment raised to a negative power whenever the second moment diverges, uniformly in time, disorder, and radius.
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The Critical 2d Stochastic Heat Flow and Related Models
Review of the proof that 2d directed polymer and stochastic heat equation partition functions converge, in a critical window, to a unique object called the critical 2d stochastic heat flow.
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